I think there's two separate questions here: First, could Khal Drogo's khalasar have swept the Seven Kingdoms by themselves?
When Dany poses this very question to Ser Jorah, he seems convinced that they would win in open battle. (I'll be relying on the books for most of my analysis, but it should apply equally to the show).
They are better riders than any knight, utterly fearless, and their bows outrange ours. In the Seven Kingdoms, most archers fight on foot, from behind a shieldwall or a barricade of sharpened stakes. The Dothraki fire from horseback, charging or retreating, it makes no matter, they are full as deadly... and there are so many of them, my lady. Your lord husband alone counts forty thousand mounted warriors in his khalasar... Your brother Rhaegar brought as many men to the Trident, but of that number, no more than a tenth were knights. The rest were archers, freeriders, and foot soldiers armed with spears and pikes. When Rhaegar fell, many threw down their weapons and fled the field. How long do you imagine such a rabble would stand against the charge of forty thousand screamers howling for blood? How well would boiled leather jerkins and mailed shirts protect them when the arrows fall like rain?” (GoT, Daenerys IV)
The problem is, as Ser Jorah notes, that the Dothraki have no experience or skill with siegecraft.
Mind you, Princess, if the lords of the Seven Kingdoms have the wit the gods gave a goose, it will never come to that. The riders have no taste for siegecraft. I doubt they could take even the weakest castle in the Seven Kingdoms, but if Robert Baratheon were fool enough to give them battle...” (GoT, Daenerys IV)
And as for that question, he thinks its likely that while Robert was fool enough to meet them in open battle, his advisors were not.
He is a strong man, brave... and rash enough to meet a Dothraki horde in the open field. But the men around him, well, their pipers play a different tune. His brother Stannis, Lord Tywin Lannister, Eddard Stark... (GoT, Daenerys IV)
So as to whether or not the Dothraki could have taken the Seven Kingdoms by themselves, I think it's debatable, but I'm leaning towards no. So long as someone with any sense in them is behind the Iron Throne, it would be child's play to starve out 40,000 men with no knowledge of the surroundings and therefore limited foraging abilities. At the very least, the Dothraki would have been unable to create a naval blockade, meaning key locations like Dragonstone, Storm's End. and King's Landings would have been well-provisioned throughout the war.
But it's worth noting that in addition to the khalasar, Khal Drogo would likely have had significant allies that would have added to his chances of victory. (I leave the dragons out of this on the fair assumption that they would have never hatched without Drogo's death.)
Viserys seems convinced that some in the realm would rise for him, so much so that he didn't even think he needed the entire khalasar.
“We won’t need his whole khalasar, “ Viserys said. His fingers toyed with the hilt of his borrowed blade, though Dany knew he had never used a sword in earnest. “Ten thousand, that would be enough, I could sweep the Seven Kingdoms with ten thousand Dothraki screamers. The realm will rise for its rightful king. Tyrell, Redwyne, Darry, Greyjoy, they have no more love for the Usurper than I do. The Dornishmen burn to avenge Elia and her children. And the smallfolk will be with us. They cry out for their king.” He looked at Illyrio anxiously. “They do, don’t they?” (GoT, Daenerys I)
Now obviously, Viserys is pretty delusional about how anxious the realm is for his return. But Robert also tells Eddard that if Viserys returned, Targeryen loyalists would join him:
"There are still those in the Seven Kingdoms who call me Usurper. Do you forget how many houses fought for Targaryen in the war? They bide their time for now, but give them half a chance, they will murder me in my bed, and my sons with me. If the beggar king crosses with a Dothraki horde at his back, the traitors will join him.” (GoT, Eddard II)
Again, this might just be King Robert being paranoid and his legendary hatred of the Targs. But we see some indications in later books that both men are right. To begin with, three of the houses that Viserys names rise against Robert's "son" Joffrey-- the Tyrells with Renly, the Darrys with Robb Stark, and the Greyjoys in their own rebellion-- and the fourth, the Redwynes, would have if the Lannisters weren't keeping their twin sons hostage.
I think Viserys was counting on Tyrell support because they were the last major house to turn against Aerys, but it's possible they would have joined out of pure ambition. The Tyrells are shown to basically switch sides to whoever looks like they have the greatest chance of victory, switching from Aerys to Robert to Renly to Joffrey. If the Tyrells ever decided that Drogo and the Targaryens had a better chance, they'd probably turn their clocks and bring the most populous of the Seven Kingdoms with them.
A Feast of Crows reveals that Viserys was right on the nose on two counts. First, Jaime reveals in a flashback that he and Tyrion found hidden dragon banners while staying at Castle Darry, indicating that they are still Targeryen loyalists. But more importantly, it's revealed that:
Dorne has signed a secret pact to support Viserys and Daenerys when they invade Westeros, and Prince Doran has been plotting the overthrow of the Baratheons and Lannisters for over a decade.
And finally, it's worth noting a notable source of support that even Viserys didn't know he had: the Golden Company.
“Which plan?” said Tristan Rivers. “The fat man’s plan? The one that changes every time the moon turns? First, Viserys Targaryen was to join us with fifty thousand Dothraki screamers at his back..." (DwD, The Lost Lord)
For those who haven't read the books, the Golden Company is an elite mercenary group operating in Essos. It's primarily composed of exiled Westerosi, has 10,000 men in the company, many of them knights, and even have war elephants. They are very skilled at siegecraft, taking several castles with ease in the later chapters of a Dance with Dragons. One of the Winds of Winter sample chapters reveal:
They have taken over the famously impregnable Storm's End.
So I guess if your answer is could Khal Drogo have taken the Iron Throne at all, rather than whether or not he could have done it alone, I think the answer is clearly yes. With the combination of his thousands of Dothraki screamers, the Golden Company, a few ragtag Targeryen loyalists, possibly the Tyrells...
...and definitely the Dornish.
Like all what if? scenarios, nothing is 100% certain. Robb Stark and Renly Baratheron were both major players who were burned because of major unforeseen circumstances. In particular, Khal Drogo and Viserys are both wild cards. I can see either one of them acting in a way that would alienate their possible Westerosi allies. But I think they had a real shot at victory.