**This is my own opinion supported by facts which formed it**. 

Id' say No, there is no evidence for it other than few curious things. 

This _Blood of the Dragon_ thing is not exclusive to Targaryens, it has existed since the day Valyrian freehold was established. 

It is something we might call a [National myth][1] which Valyrians created to set themselves apart from rest of the world.

We have to learn why did Valyrians needed such a myth? 

###Civilization envy

Valyrians, despite their later successes, were in fact not the first people to adopt civilization or to found an empire of conquest. It was actually the Ghiscari who managed to do that. 

> AS WESTEROS RECOVERED from the Long Night, a new power was rising in
> Essos. The vast continent, stretching from the narrow sea to the
> fabled Jade Sea and faraway Ulthos, seems to be the place where
> civilization as we know it developed.
> 
> **The first of these** (not withstanding the dubious claims of Qarth, the
> YiTish legends of the Great Empire of the Dawn, and the difficulties
> of finding any truth in the tales of legendary Asshai) **was rooted in**
> **Old Ghis**: a city built upon slavery.<br><sub>**_TWOIAF-The Rise of
> Valyria_**</sub>

Ghiscari soon started expanding after formation of their city state and its fabled lockstep legions. 

> Old Ghis and its army proceeded to colonize its surroundings, then,
> pressing on, to subjugate its neighbors. Thus was the first empire
> born, and for centuries it reigned supreme.<br><sub>**_TWOIAF-The Rise
> of Valyria_**</sub>

In the meanwhile, Valyrians were limited to their peninsula, without any dragons or any civilization. 

Daenerys had it rubbed in her face as well when she showed pride in her Valyrian roots in front of the Ghiscari. 

> Dany knew she would take more than a hundred, if she took any at all.
> "Remind your Good Master of who I am. Remind him that I am Daenerys
> Stormborn, Mother of Dragons, the Unburnt, trueborn queen of the Seven
> Kingdoms of Westeros. **My blood is the blood of Aegon the Conqueror,
> and of old Valyria before him**."
> 
> Yet **her words did not move the plump perfumed slaver**, even when
> rendered in his own ugly tongue. "**Old Ghis ruled an empire when the
> Valyrians were still fucking sheep**," he growled at the poor little
> scribe, "and we are the sons of the harpy." <br><sub>**_ASOS-Daenerys
> II_**</sub>

So as evident, Ghiscari at least viewed Valyrians with scorn due to the pride that theirs was an empire and civilization far older than Valyria's. 

###The myth begins

Once the Valyrians had learned how to tame their dragons, they set forth to carve their own empire. Since they had dragons which no one else had, what better icon was there to form their national myth?

> It was on the great peninsula across from Slaver’s Bay that those who
> brought an end to the empire of Old Ghis—though not to all of their
> ways—originated. 
> 
> Sheltered there, amidst the great volcanic mountains known as the
> Fourteen Flames, were **the Valyrians, who learned to tame dragons and**
> make them the most fearsome weapon of war that the world ever saw. 
> 
> **The tales the Valyrians told of themselves claimed they were descended**
> **from dragons and were kin to the ones they now**
> **controlled**.<br><sub>**_TWOIAF-The Rise of Valyria_**</sub>

This is what is said about origin of Dragons:

> The Valyrians themselves claimed that dragons sprang forth as the
> children of the Fourteen Flames, while in Qarth the tales state that
> there was once a second moon in the sky. One day this moon was scalded
> by the sun and cracked like an egg, and a million dragons poured
> forth. 
> 
> In Asshai, the tales are many and confused, but certain texts—all
> impossibly ancient—claim that dragons first came from the Shadow, a
> place where all of our learning fails us. These Asshai’i histories say
> that a people so ancient they had no name first tamed dragons in the
> Shadow and brought them to Valyria, teaching the Valyrians their arts
> before departing from the annals.<br><sub>**_TWOIAF-The Rise of Valyria_**</sub>

So it is evident, that Dragons had existed long before Valyrians learned to tame them. If they were actually descended from dragons and all they needed was their blood to tame the dragons, Why didn't they it sooner? Why didn't they do it when Ghis was expanding its Empire and Valyrians were a small isolated people?

The dragons were not even exclusive to the Valyrian peninsula either. They were found all over the world. If Dragons could give birth to humans, why is it there was no other such race any where? But if indeed we are to believe that Dragons did originate in Valyria and then migrated elsewhere, why is it that the Blood of the Dragon couldn't stop their migration until they learnt how to control them?

> But there were dragons in Westeros, once, long before the Targaryens
> came, as our own legends and histories tell us. 
> 
> If dragons did first spring from the Fourteen Flames, they must have
> been spread across much of the known world before they were tamed.
> And, in fact, there is evidence for this, as dragon bones have been
> found as far north as Ib, and even in the jungles of Sothoryos. But
> the Valyrians harnessed and subjugated them as no one else could.<br><sub>**_TWOIAF-The Rise of Valyria_**</sub>

The second part of the myth was the way they looked, which was used to emphasize that Valyrians were different from rest of the humans. 

> The great beauty of the Valyrians—with their hair of palest silver or
> gold and eyes in shades of purple not found amongst any other peoples
> of the world—is well-known, and often held up as proof that the
> Valyrians are not entirely of the same blood as other men.
> 
> Yet there are maesters who point out that, by careful breeding of
> animals, one can achieve a desirable result, and that populations in
> isolation can often show quite remarkable variations from what might
> be regarded as common.<br><sub>**_TWOIAF-The Rise of Valyria_**</sub>

Physical features do not necessarily mean that one race is not part of humanity but something else. We know that in Planetos, different races exist which can be correlated to White, Black, Brown, Asian people in our own world. Given the physical differences between all of them, there is no way to assert that one race maybe uber-human or inhuman. 

###Are there any shards of truth in the myth?

But we have to note the curious attraction and bond between the Dragons and Valyrians. 

> This [Selective breeding and incest] may be a likelier answer to the
> mystery of the Valyrian origins although it does not explain the
> affinity with dragons that those with the blood of Valyria clearly
> had.<br><sub>**_TWOIAF-The Rise of Valyria_**</sub>

In any case, we do know that Valyrians used blood magic to bind to dragons so it maybe that this was the factor behind this strange affinity. 

We also have to note that Targaryens are noted to feel heat less than normal humans. Examples are Daenerys Stormborn and Aegon V Targaryen but then again we know how sweaty Viserys III got in Dothraki plains. 

Also as you have noted, [Daenerys and other Targaryens have given birth to malformed children with dragon-like features.][2]

###Conclusion

 1. Valyrians needed some myth to make themselves appear superior to other men. 
 2. Valyrians existed prior to controlling dragons, most likely in humble circumstances. 
 3. There may be some truth in the myth which can't be explained but could be effect of the magic that ran Valyria. 
 4. We do not know for sure yet as GRRM hasn't yet explicitly confirmed or rejected it.


  [1]: https://en.wikipedia.org/wiki/National_myth
  [2]: https://scifi.stackexchange.com/a/135444/54887