I would for sure get that done as soon as possible. You probably don't have to buy plates for it (at least in IL), but getting that title into your name makes you breath easier.
In IL, you get the title and then you get license plates. The title transfer fee is something like $30, then you pay the sales tax (on old cars its $25, for now anyway). The plate fee is $151 and is good for a year unless to get an antique (very restrictive but cheaper I think)) or extended antique plate (drive when ever you choose between March 1st and Oct 1st, then very restrictive the other 6 months, same cost as regular plates). Those the plates are good for 2 years.
Any hassle happens when you put the title in your name. If the state decides you are the lucky person they want to check the numbers on, the plates wait until the Vin check has been done. Once you have a title in your name, buying the plates just costs what ever the plate fee is. The last 4 hot rods I've done I get titles in my name as soon as I can, then when I'm ready to drive it, I buy the plates and can drive it that day. In the past, doing both often resulted in not getting the plates until they cleared the title stuff first, that could have been a delay of a week or two, or a few months. It seems as though getting the title only first results in much faster action. The state gets more money from plates then they do title transfers.