Could a drow be a member/believer of the Silver Flame?
Highly unusual but why not? I'd suppose that it is the work of the Silver Flame pilrims, that your drow is an immigrant or that his tribe/clan/nation are tied to a cult that reveres the couatls-not unknown in Xen'drik.
Why not? Elves and shifters do. You just need a story on how the drow learned about the Silver Flame and came to appreciate its tenets. That should not be too hard, since its followers travel to Xen'drik, and the drow character's tribe could always have captured one. It would also give your character a good reason to travel to Khorvaire: to learn more about the faith at its source.
One of my favorite PCs was actually a goblin cleric of the Silver Flame, a member of the inquisition. He might have had some arguments about whether or not he was worthy, but nothing that a good smiting of evil could not cure 
[He actually spend most of his time on Xen'drik for a reason, but he was not particularly bright.]
The question I'd have is if there are drow that already DO follow the Silver Flame, and if so, what form it takes. The Silver Flame is ancient. The Ghaash'kala orcs followed the Binding Flame long before humans ever came to Khorvaire. The Khaleshite crusaders of Sarlona had their serpent cult, and their shulassakar leaders were something the Quori exploited to turn others against them. Tira Miron may have founded the modern Church of the Silver Flame, but there's lots of other paths one coulld take. I might spin it off of the Sulatar culture - drow who have heard the call of a different flame than the Promise of Fire, and follow a mmore benevolent path than their kin.
Awesome ideas. Thanks. I am really learning to appreciate Eberron more everytime I adventure there. Whether DDO or my PnP campaign.