One of the guys in our club uses tape with wraps. Actually, he's the only one in the club who uses wraps. He's not mentioned any problems. Sorry, but on this thing, second hand info is the best I can do. [&:]
Like AP, I only have second hand info but it comes from some one who fletches a lot of arrows.
She says she has excellent results with the tape sticking to the wraps.
We have some aluminum arrows that we can NOT get feathers to stick (tried several different glues). She suggested putting wraps on first. Haven't gotten it done yet though...