You can definitely make a drow character work.
There's always ways to work around their sunlight sensitivity, but that's probably best handled through background story.
We have a drow in our party (Not evil) who has been on the surface world for near a 100 years (Through enslavement by a fire giant) and has adapted to its harsh light.
It's workable and I love the character itself.
And it's definitely no Driz'zt.