Yes you can if you are careful, but please don't do this. Think it through. You can remove the laminate counters easy enough. Granite prices are at an all time low, provided you're not too picky. Should you not decide to go with granite, you could set up a 3/4" plywood base for a tile countertop and lay down marble or granite squares. These installations usually look less than professional. If you really want tile, you should shop around a bit and see where you can get your cheapest slab granite prices. Make sure you can trust the installer and their prices. A lot of times that's where you spend most of your budget, on the install.

And as you thought, the sink becomes a problem, which is why most installations you will see will involve undermount sinks under granite slabs.