Only if you make it so. but even then...replace Elistraee with any good deity and continue.Shrug, im just saying there are ten thousand easy ways that make sense for Drow low level pc's just like what I describe. It's as easy or difficult as the DM wants.
If you dislike the idea of Drow PC's starting on the surface no amount of story is going to make you love it. If you don't mind low level Drow on the surface, any of those ten thousand will work.
Same can be said with any race or class.
It irks me to heck and back for players to play Lizard Men characters, I don't allow them. I just don't act like it's because it is impossible for there to be a good reason for a Lizard Man pc, I just don't like them to the point of it ruining my fun,so nope, can't be one. Though I did cave in once for a Lizardman Druid..........