Most tape doesn't stick well to foam anyway! Seriously, it's a pain to keep it in place, depending on the foam and tape you use. Even if its a simple design, it will help you out a hundredfold if you have a pattern from the tape. Then you can shape it right and won't have many gaps or bumps
I'd say try the tape you want to use on a scrap piece of foam, but most I've ever used has been a hassle to keep on the head as I'm making the pattern for it. Of course anything is possible, but if you're worried about the foam getting ripped, just wrap plastic wrap around the head as snug as you can, making sure it goes in any dips and curves over any outward parts, then apply the tape on top of that. But I've never had a problem, and cutting the tape off doesn't hurt the foam a whole lot, plus it will be covered with fur anyway