@psm16 Youc an definitely do that. You will just need to make sure you have enough space between your joists (height and width) If you do, then you will be golden. You will end up attaching the box to your joists. Exactly how you want to do that, is up to you. But if you do that correctly it’ll be even with your drywall. Then you can fill the minor gaps between the dryall and the box with something like caulk. Once painted it should be fairly seamless.
Another option would be to buy a 1/4″ thick piece of drywall recess the driver 1/4″ less than you normally would. Add the 1/4″ drywall to the outside of the box. Once it is in place, you can finish your drywall seams link normal. If you want the speaker to be covered, I would recommend making something out of white spandex or speaker grill cloth.