If you have already used your balance to pay your bill, it won't be credited since you've already used it. But if you add the money to your account before the due date and then change your plan while there is still money on your account, it should be...
The SIM card will work. Public is a prepaid service. So you just have to buy the sim, activate it, choose your plan (and pay for it), and there you go. All set.
The most I've received is $1, so it probably will take a while to get to $20. If you have the time to do it, then go for it. I have the time to do it, just not the patience.