The major rental companies (Avis/Hert/Sixt/Europcar) will pass on your info to the authorities and not pay the fine for you. The authorities often choose not to follow up on some violations because the effort is not worth it. However, if they do contact you, it is advisable to respond.

Contrary to popular belief above, US personal checks are accepted in many countries. I've personally deposited checks into my German and Indian chcking accounts. It takes a while and is not very popular with the banks, but it does work.