I took full payment and he took the car.
Yes you need title. If you have existing plates and bill of sale you should be able to drive around just fine.
IL law gives you 30 days to register if I recall correctly.
What plates would you put on the car? Most sellers aren't going to give you their plates to use temporarily. I'm also pretty sure there's a decent penalty for driving around with plates that aren't registered to a car, though I guess if you don't get pulled over it's not a problem.
I've sold a couple cars bikes with liens and it took anywhere from 2-4 weeks to get the title.
IMO there's no way to drive it without registration without possibly getting a ticket. I've been pulled over a couple times in a vehicle I had just bought and the police said if you don't have a plate it's illegal, and if you are driving on a plate that's not registered to the car it's illegal. I had the bill of sale and explained that the BMV tells me I have 30 days to register it, but neither officer cared.
For the 3 vehicles I sold that had loans on them, the purchaser did not drive it until I gave them the title