It's really not about the skin, it's about the nerves underneath the skin. If that skin is laid over functioning nerves, then yes, you will likely have some sort of sensation. (Now, once the nerves are cut, those might *not* grow back.)
I have a scrotal skin graft - scrotal skin that was cut completely away and then stitched back in a new place - and I do have some limited sensation, but it's largely pressure/fullness rather than the sensation that I used to have from the scrotum. I believe that that is because the original scrotal nerves have been moved around; the graft is now sending nerve signals from the nerves underlying the place that it ended up, instead.
(On the other hand, once my brain remapped that the nerve signals from, say, the penile glans were coming from the clitoris, it became hard to imagine that I'd ever felt anything else from those nerves. And the glans was also severed completely and restitched in a new place, but over the existing nerve bundle; I have, well, let's just say "more than full sensation" from that area.

)