My home came with drywall walls and ceilings throughout. I think I have one pantry wall that is not wallboard. And yes, you can replace the walls you might already have with wallboard. It is a very labor- intensive job, but people claim the results are worth the work.

They make a special 1/4" thick gypsum board that's designed to overlay an existing wall. You could do the job yourself by green nailing the board to the existing wall and have a professional come in and finish it. Some of the problems you will run in to are bringing the electrical outlets flush, moving out the cabinetry and countertops, and finishing around the window/doors.
Doesn't cost anything to get a quote from a local remodeling contractor.
But yes, you can overlay your walls with drywall.