It doesn't seem so. I think it works like this: All blades which glow in the presence of Orcs are Elven, but not all Elven blades glow in the presence of Orcs.
I don't recall reading anything in the book which would suggest that all Elven blades glow, but it is difficult to prove a negative - for instance, there wouldn't be a passage that said "The Orcs drew nigh, and Legolas drew his sword, which wasn't glowing because it didn't do that kind of thing."
"...being the work of Elvish smiths in the Elder Days these swords shone with a cold light, if any Orcs were near at hand".
- The Fellowship of the Ring
This passage could be interpreted as saying that all Elven blades can glow, but that's not how I understand it. Consider the following sentence:
"Being the work of a talented carpenter, the tabletop was beautifully inlaid with delicate, hand-carved, interlacing floral patterns."
After reading this sentence, do you believe that talented carpenters are only capable of making tabletops with interlacing floral patterns, and nothing else? Of course not. The sentence really means "if a tabletop is beautifully inlaid with delicate, hand-carved, interlacing floral patterns, the person who made it was probably a talented carpenter".
Applying the same logic to the quote from Fellowship of the Ring, we can probably say that it is really telling us: "If a blade glows in the presence of Orcs, it was probably made by Elvish smiths, most likely in the Elder Days". Assuming that this is, in fact, the case, it seems likely that all blades which glow in the presence of Orcs are Elven, but not every Elven blade can glow.
However, we can look to the movies, despite all their flaws, to corroborate the idea that not all Elven blades glow. Here, too, it seems to be the case that some Elven blades, like Sting, glow, but most of them don't. I came to this conclusion after finding the following pictures and videos. I made the assumption, which I think is quite reasonable, that Legolas, Haldir, Elrond, and the Elves at Helm's Deep, the Battle of the Five Armies, and the Siege of Barad-dûr were armed with Elven blades.
If my assumption is correct, and if the images and videos below are reliable sources, it would appear that glowing is not a natural byproduct of Elven craftsmanship. That is to say, a sword won't glow in the presence of Orcs simply because it was made by Elves; the Elves have to deliberately make it in such a way that it glows. For whatever reason, they usually don't imbue their swords with the ability to glow - the actual number of glowing blades in the story (both in the books and in the movies) is relatively small.
On a side note, Narsil, which was originally made by a Dwarf, doesn't glow in the presence of Orcs, even after it is reforged by the Elves of Rivendell and christened "Andúril". This suggests that neither the initial creation of a sword by Elves, nor the reforging of a sword by Elves, is enough to make it glow around Orcs.
By way of comparison, here is what Sting looks like when Orcs are near:
Note the total lack of glowing in the following images and videos:
Elves and Dwarves at the Battle of the Five Armies.
Elven army at the Siege of Barad-dûr.
Two pictures of Haldir and his sword, at Helm's Deep.
Two pictures of Legolas and his knives, at Helm's Deep.
Unidentified Elf and sword-staff, at Helm's Deep.
Unidentified Elf and sword, at Helm's Deep.
Elrond and his Elven army at the Siege of Barad-dûr.
When the regiment of Elves who came to Helm's Deep draw their swords, none of them seem to be glowing (the sword drawing happens at about 0:40 into the clip):
Legolas' knives don't appear to be glowing in the Battle of the Morannon (i.e., the Battle of the Black Gate):