I do not think wallpaper would hold up on a kitchen counter top. But they can be painted. Use either Giani, or Rustoleum counter top paint.
Diane at in my own style has a great tutorial on painting old counter tops.
It will not hold up to every day use. There are many kits on the market today to refinish counter tops. Head to your local hardware store to see what is available. Kits usually have everything you need and easy instructions to follow.
Wallpaper would notbe durable enough to withstand use. Cupboard doors maybe but not the counter.
I think you can use wallpaper. It must be properly sealed. If folks can use paper on floors you surely can use it on a countertop.