There should be no problem as long as the car's trunk is large enough. Here are four examples:
My own car is a 97 Taurus 4 Door Sedan. My ECV can fit (completely but snugly) in the trunk. To make it easier I normally will put the ECV seat on the rear seat of the car.
When renting, the same ECV will fit (again, snugly) in the trunk of a Buick Century.
When I have rented a Buick Le Sabre it was easier to get the ECV into the trunk.
Renting a Buick Park Avenue, not only was there room for the ECV, but for lots of other items if needed.
In relation to this. If you are going to be at one of the Deluxe hotels the valets will assist you in loading/unloading the ECV as well as disassembly/assembly. Some of the more experienced valets are quite good at it. Normally there is a $6.00 per day valet parking fee; this is waived if you have a handicap hang tag. If you do not have a handicap tag, they generally will still waive the fee but will grumble at you. Note that the valets are tip positions and they do not get a commission on the valet fee (it is all gray for Disney). I will normally tip $2.00 both in and out if my ECV is not involved. If they take care of the ECV I will usually tip $5.00 both in and out. If they do not offer to assist with the ECV (and kind of ignore me), not only will I not tip, but I will discuss the matter with a supervisor.