Not to steer anybody wrong but, I have been flying in county parks for 4 years and never have been asked for my AMA card by anyone. This is not to say you shouldn't get the card but, it should help you relax a little on the tecnicallities .
I would call AMA or look it up on the web, and get as much information as you can. Some county parks ban RC planes and some don't . I have been lucky enough to find a bunch that don't. When I do find one that does, normally there is a huge sign stating NO RC AIRCRAFT ALLOWED.
Can you fly without AMA , I would say most deffinitely yes. But you will not be insured in the event you hit someones car or hit someone period.
All jokes aside get AMA before you fly , it makes everyone flying RC craft feel alot more secure.