No, the '80s rock band did not use this as a tour bus. REO, pronounced like Rio, was founded by Ransom E. Olds after he was forced out of Oldsmobile. Besides cars, REO made commercial trucks, among them Speedwagons. According to Barrett-Jackson, this Speedwagon was originally owned by a couple named Mose and Lillian from Louisinia. They used it to travel with a carnival selling prizes and kewpie dolls.
An association with actor McQueen can multiply the value of a machine.