Yes you may visit any resort you wish. You will be given a visitors parking pass good for 2 or 3 hours. You are not allowed to use the pool at resorts you are visiting, otherwise you may do pretty much anything you want.
I believe the only time you will get a resort upgrade is if you have a confirmed reservation they can not meet at your resort or any other resort of the same level - ie no rooms available at an AllStar or at POP - then you would get upgraded to a moderate resort.