Well, it depends on how much is unsupported. Is it more than 2-3 inches? Can you post a picture? I've done sheetrock returns in remodels of old houses where every outside stud was rough cut and needed nailers to make a finish surface. We had some pretty heft gaps and it wasn't an issue. Granted we also were the sheetrockers so we couldn't complain too much about the 'other guys' work.

Yes. You can hang a blind from the vinyl jamb. Make sure to pre-drill before you screw. If it's not solid enough, just use a longer screw and you should find some wood. Good luck!

No-casings and painted sheetrock returns are the right look for a modern house, and the major brands of windows have all gotten on board with all-fiberglass or for Andersen, all fibrex, windows, this class of windows having relatively shallow frame depth, and all offer dark colors same outside as in, to achieve this popular new look in "modern." The #1 favorite color is black, followed by dark bronze. To do it right, the carpenter needs to properly shim the opening before the rockers get there, so reveals are consistent all around. Insider Carpentry channel on YouTube has a great vid on how to do this right. The rockers need to mask well, then use a tearaway bead at the window side, and a good corner bead at the outboard sides. The best look, IMHO, is to have a 3/4" thick sill at bottom with the same window reveal as the sides, so the bottom of the opening is not shimmed in as much as the sides. To get this right, the window sits up on shims at installation time and the bottom of the opening is only shimmed to get it dead level and flat for the drywall corner bead. That sill gets no apron under and has to have a good plate-like bed. Anything more than 3/4" looks to beefy. Sills should have tiny returns. Here is a 3D render done in Chief Architect of a window with sill and another without. The windows are modeled at the same dimesions as the all-fibrex Andersen Series 100, the wall is 2x6 framing, and the depth of the returns to the drywall face is 4-9/16". Note the very shallow bullnose on the sill edge, and the small return. A painted wood or stone, metal, or composite sill is going to be more durable and easier to wipe clean than painted drywall, no matter the paint. And as for the dust on those vertical returns at jambs, or horizontal across the head, and durability, you have all kinds of drywall corners eleswhere in the house. Why are corners at windows going to behave differently. If your builder has not done these no-casings openings before, think twice before asking him to do it. If he has, insist on seeing examples of work. You don't need to be a first time event for the builder, his carpenter, or his sheetrocker.

Budget Vs. look? I’d say it’s both. Like Beverly mentioned above, my MIL has had drywall returns with marble sills for 35 years. To me they still look great...classic and timeless. They were done well at the time, and it shows. Most trim I see going up these days does not any look better, IMHO. Especially if you’re trying to achieve a clean, contemporary, but somewhat “timeless” look. However, I also have several rentals with basic vinyl windows and drywall returns all around. Those were done for budget, and for the ease of a quick paint touch up when it’s time to turn them over.