I would not see why you can't. MDF although a man made product it very strong and stable. It is used because it is cheaper but it not necessarily inferior to solid wood. It is in many ways better.
I haven't tried to attach cushions to MDF before, but I have built custom countertop bases out of MDF before, and didn't have any trouble getting it to adhere to itself and to other materials with various, readily available adhesives.
alright just curious i hope nothing bad happens to the rails when we take the old cushions off though. wish i had the money for a nicer table :-( but i have to many kids i have to buy toys for.