Sure. You can make a quilt out of anything. There are art quilters who make quilts out of Tyvek (the stuff they wrap houses with to make them waterproof), so polyester seems perfectly reasonable. You'll want to be very careful when ironing to have it on a low setting so you don't scorch your fabric & I'd recommend making a small practice sandwich before quilting because the different fiber content might look a little different when you quilt it.
I'd also strongly suggest using poly thread to quilt it if you want it to be durable. Otherwise, over time, the poly fibers will cut into the cotton thread & weaken it until it eventually snaps. Won't happen right away, but will happen eventually.
I'm not so sure about "in the car quilts". If you mean something to cover the seats so they don't get all those crumbs everywhere, that'd be fine. If you're thinking about using them to cover the children with in the car, it depends on their ages. If they're in a booster, poly is definitely okay. If they're in a car seat, they might get a bit too warm & would have difficulty getting the quilt off of them. If they're babies, I would not ever suggest poly fabrics on top because the baby can overheat. Using them on the floor/ground should be fine at any age.