Hi Diane, yes you can. Here is a post about that: http://www.hometalk.com/144797/i-finished-painting-my-kitchen-countertops-this-weekend
Just make sure to first clean with TSP and lightly sand taking of some if the slickness. And most importantly, paint a coat or two of oil based solvant primer. Let that dry overnight, It'll give the countertop some tooth for the paint to adhere to. Then your're ready to paint. I always paint 3 coats of a water based poly after the faux finish to seal. I like the satin finish rather than the gloss. But whatever you like is what you should use. It's your masterpiece.
As someone who does microbial testing, I would be careful with this type of finish. While there are great products as you can see by Miriam's post, you simply cannot scrub this finish clean as it will eventually wear down exposing what ever finish it was that you covered. Knowing that, you may be inclined not to clean as well as you would with the original surface.
Also as a CAPS contractor who does specialty work for aging in place adults, we are taught not to choose colors that can hide food partials. Light color tops are often the choice in those homes. While many people will choose a blended top with lots of colors this oftentimes can come with risks.
But you can paint laminate tops. Just be careful when following directions for the finish you choose. Clean and prep the tops well. And most of all use cutting boards and protection on the counter when prepping food.
If you decide to do this, please provide us with your before and after photos!
I am buying a home with a redish color countertop. The color is fine with me but my daughter can't stand it. I am wanting to do most of the painting and such before moving into the house. So I thought if absolutely must, would go this route until I could afford other.
Good luck with your new home, Diane. Keep us posted on what you decide to do.
I used the technique I posted above 10 years ago over formaica in the kitchen and ceramic tile in the bath. Every 2 years I add another coat to satin poly and my countertops look beautiful. My friends and guest cannot believe they're not granite. I scrub them just like I would if they were not painted. Just don't use brillo or comet as it is abrasive. But anything else I have used with no problem once the poly cures.