When applying for a monster race it is usually taken with a grain of salt that you cannot interact with portions of the server, usually on pain of death.
It is however, in no shape or form a hinder to interaction based upon the fact you cannot go to upper, so long as you have people who can go up there for you. Having played a monster race now, and in the past had some, there are ways to get around the system.
If you are willing to risk it, High stealth or Invisibility can get you navigated around, and the NPCs will not hostile you, granted you would likely need a DM as mentioned above.
Also a key thing to bring up, Drow do -not- look like elves when fully clothed/helmed. They are stockier and shorter than your average elf, as well as there is ample helmed elf harassment, having played one just the other day, who was stopped numerous times by PC law enforcement. Just because you don't see something does not mean it doesn't occur.
That being said, there are always IC ways to subvert that via becoming a citizen, or simply finding ways to interact with PCs beyond Sanctuary. While it is a fair portion, Upper is -not- all of the server, and New Dunwarren is for the better sake of the place, "Hibernating".
Drow are loathed. Drow should revel in their loathing, and wandering into some stank filled hovel of slaves to speak with one should be low on the priority list.
There's some credence to the idea of disguises, but as said time and again, Sadly NWN is just not set up for disguises. Even if you were fully clothed, in a helm, and allowed to walk the streets, there's always that M word that gets tossed about.