You mean corner bead. No. Don't put that in an inside corner ever.
You want it to be 100% sure it never falls down? Use construction adhesive. PL Premioum. Screw it in. Next day you can remove all your screws if you want to. Just makes it a huge ***** if you ever need to remove that section. You will pretty much need a chisel.
You want to screw in that perimiter edge? If you are ready to buy corner bead because it's cheap, buy a bundle of the metal 2x4, or 1x2, whatever is near you and cheaper. Cuts with snips. Screws with same screws into wood. And you can make yourself some perimiter cross braces. I would not do this generally. But one must when one wants **** stronger. I've done this too. Sometimes when you are not sure of durability, you add braces and glue lol.
It's not rocket science really. If you must do it this way, don't let it hold you back. And here, in NYC, we Sheetrock every usable space to make it usable, livable, rentable. It's cheaper than drop ceiling, everyone knows where to buy repair parts, and nearly everyone can patch it. No point being afraid of someday needing to make a hole or even ripping it all up. My garage is sheet rocked with all plumbing and wiring hidden. So is my basement. So is every rental basement. One I did drop ceiling, but that was because its a rental, and I wasn't going to redo all plumbing and electrical to reclaim 2". If all was hidden, I would of Sheetrock that one too.