Not necessarily. Tire machines will work up to a certain designed size limit. A place that only sells car tires may not be able to mount your rear tractor tires unless they do it by hand and the personnel may not have the skills or tools for the job -- there is risk of damage to the bead area or the rim if you just try to force the tire on with a crowbar and hammer or something.
If they do sell tractor tires, they may not want to mount tires you bought elsewhere without charging you a nice price for the service.