Yes, in most cases they will. You can work with a UF academic advisor, to determine which PA CC classes they will accept.
It’s based on your major, and which college you apply too. For example, if you want to apply to the Mechanical Engineering department, you would work with an advisor in this department to review your PA classes and determine which ones they will accept. You can show them your proposed clases, so you know ahead of time which classes will be accepted. UF isn’t too picky…a Calc 1 class is a Calc 1 class.
It’s a lot easier transferring from a Florida CC or public University, as Florida has state wide standards for class names, etc.
Personally, I would save the money and attend a CC, than one of the regional PSU campuses (unless you commute from home), if you DON"T plan on graduating from PSU. Just confirm that those classes would be accepted. 
Good Luck!