Actually, they will not send you a check. Furthermore, the myth of paying more and not cashing the difference (b/c then they cannot put you in the system) is just that - a myth.
Not sure about your city/state law, but in OH you bet your sweet @$$ he can: no plate = cannot drive. If you get caught w/o the plate = ticket+ jail + impound.
And honestly, you really gonna whine about $35 ticket? No offense, but pay the ticket and don't park on the sidewalk. I understand where you're coming from (I park my bikes on the sidewalks sometimes), but you've learned your lesson and actually got off pretty easy since he really could have impounded your bike...
It sucks, but I don't think it would be worth your time and money to fight $35 ticket. Do what "spoke" said: pay it and go ride...