I think it probably will as it's a classic, the name of queens and saints, etc. I was born in the 60s and several school contemporaries were named Anne or Ann, (and half the class had it as a middle name!) I also knew several Annes of my mother's generation and a bit older, but from about 1970 it seemed to fall out of favour. It's probably due to come back soon, then!
I do prefer Anna though personally, it is one of the few names that is actually a timeless classic, ie from the name Anna you cannot tell the likely age of the person at all.