[alantf]

First question :- How handy are you with tools? If the bags are vinyl, my first thought is "low melting point", so I really think you should protect them from the heat if you don't want to replace them pretty soon. If you're the least bit handy, & have a drill & a pop riveter (a riveter is not expensive) you can get a piece of aluminium cheap enough from any local hardware store, & it's only a 5 minute job to cut it to size (you'll probably be able to borrow the tinsnips off someone) & rivet it under the bag. A few (hopefully very few) dollars spent now might save you from having to pay out for new bags.
Second question :- Are the bags really floppy? Mine are real thick leather, & even if I push hard, I can't push them into the wheel. Might I suggest that you try to push them (really hard) into the wheel. Even if there's the slightest suggestion that they will touch the wheel, then yes, you do need supports. I was lucky, & don't need supports, but each type of bag is different, so I don't think that there is a definitive answer without first checking.
I bet that once you get the bags sorted out, you'll wonder how you ever did without them, & next Christmas you'll be asking Santa for a back box & rack.
(by the way, Santa brought me a magnificent digital tyre pressure gauge!)