Recently bought a car at a dealer in Wisconsin. They took care of everything, tax, title, registration. IIRC the tax was different for cook county Chicago vs cook county suburbs, but they were able to look up the correct percentage.
They gave me WI temp plates (they also said they usually have IL temp plates but were out at the time).
The way they made is sound is that not every WI dealer has access to the IL system, so I would definitely check with the dealer you are going to.