No, it does not.
There are a few power wheelchairs that fold for transport, but the great majority do not and none of the rental ones do.
This is a link to more information about the Jazzy Select:
http://www.pridemobility.com/jazzy/jazzyselect.asp
You would need to use WDW transportation with a power wheelchair - WDW buses, monorail and larger boats. There is more information in the disABILITIES FAQs thread. You can find that thread near the top of this board or follow the link in my signature.
if you want to transport by car, you will need to rent a
scooter (
ECV). Apple has a smaller GO GO Elite scooter that should meet your needs. There is a 3 and a 4 wheel version available. Those smaller scooters are quite a bit more maneuverable, especially the 3 wheel model.
If you have never used a power wheelchair, I would highly recommend NOT renting one. (You can ignore the next 3 paragraphs if you are experienced).
They take more practice to learn to drive than a scooter - mostly because everything is controlled with a single joystick. It controls speed, going forward, going backward, turning - all with the one joystick at the same time, depending on how far you push it and the exact direction you push it. For example, if you are pushing the joystick forward, but at a bit of an angle, you will turn. If the wheelchair is turned on and the joystick is bumped, it will go in the direction the joystick is bumped.
Compare that to a scooter where steering is controlled with a yoke - kind of like a bicycle handlebar in how it works - and a throttle that controls speed. In order to go forward, you have to actively operate the throttle. If you don't activate the throttle, it won't go, even if you bump the yoke. You need to actively change a control that coverts it to go backwards, so it won't go backwards by mistake.
For those reasons, most of the rental companies will only rent a power wheelchair to someone who has experience. Even if a company will rent one, I would still advise against it. There is more information in post 2 of the disABILITIES FAQs thread. You can find that thread near the top of this board or follow the link in my signature to get there.