Yes it can be done, you can cut a wrap groove as I do it all the time.
I try to talk people out of it as usually the handle is a fancy piece of wood that was meant to be seen and cost more than a regular $2.00 piece of purple heart or maple. I made a cue with exibition grade curly Koa that cost me about $100.00 and I had someone ask me if they bought the cue would I put on a wrap. Sure I could do it but the value of the cue goes from $1200.00 to $900.00.
Will it change the hit? I do not think it would.
Sending cost in PM.
AB