That's a good question. I've never had the need to hang a back drop of any kind. Depending on how heavy the backdrop is - it might, but I bet two of them would for sure - and they are pretty cheap if you buy two of them together, so I think that would be a better bet. But the legs are pretty sturdy and do go out far enough to be very stable. Sorry I don't have a better answer for you on that one.
This stand is great for lightweight items, such as lights, but I think the legs are too short to properly support anything large. It might work inside, but would not be stable outside if there was any wind where you set up your shoot.
Those screens are very light so weight would not be a problem. The problem is going to be height. This is a six foot stand and your screen is seven foot tall. You could alway hang it in landscape orientation, but it would have to be pretty much at maximun extension in order for the screen to not be pushed out at the bottom by the legs. If this is something you plan to use regularly you should probably go ahead get a nine foot stand.