I always leave my chair with the CMs and there is no problem with it being there ready for me when I get back. I would make sure to bring any bags or personal belongings that you keep on the chair, though.
I was at MK yesterday with a friend in an electric wheelchair and they were very good about the wheelchairs and even making sure our temporary wheelchair she had to transfer to was there to get us off the ride. We had to leave her purse with the cast member at Space Mountain and they made sure it was in her chair when she got off.
Not electric wheelchairs, but ECVs (often called "mobility scooters") are available first-come/first-served in the parks. Most guests opt to rent one from an offsite vendor to be guaranteed as well as having it for to/from the parks and around resort. There may be a couple of off-site wheelchair/ECV vendors who do rent actual electric wheelchairs; my understanding is this may be limited to guests who use one in everyday life at home but opted not to travel with it.
If you have a rather "generic" looking manual wheelchair, I'd recommend tying a scarf to a handle or hanging a bag on the bag (without valuables, maybe an extra sweatshirt or such) to make it easily identifiable. But yes, you can leave the chair while on an attraction and you do not need to leave a member of your party to watch it.