Will dry finish change as beer ages?

First gravity reading on my first AG brew (IPA). Gravity down to 1.012 from 1.058 in 8 days. Drank the sample from the hydrometer tube and it tasted and smelled good, however a pretty dry finish. My question, as the beer continues to age (I will dry hop in primary in a week, and sit on hops for a week for 3 weeks total prior to bottle) will it continue to get even more dry or will the finish continue to taste like it does now?

I wouldn't fret too much right now. After it's aged a bit, and carbonated, it will certainly smooth out - and that "dry" taste will go away. Have a beer and don't worry about it.