If I pay the money, will I avoid a criminal conviction?
You must speak to a criminal defense attorney in order to find out all of your options. A good rule of thumb is to contact the casino or party to inform them about insufficient funds. You will be surprised at how willing creditors are willing to work with you if you are upfront about the situation.
If the DA has the case, then you need to contact them through an experienced attorney immediately. It is best to have a lawyer negotiate for you because maybe the restitution could be lowered or the case could be entirely dismissed.
The longer you wait, the more it is likely that additional fees will be added and more charges will pile up. Call a lawyer to get a full explanation of your rights.