Can I put 6” recessed cans into 7” holes?
No problem at all doing this. But I would come up with a way to fill in that gap you have. It will allow drafts and dust penetration. Personally, I'd square the opening in the ceiling, take a new piece of drywall the same size as the hole and put the hole for recessed can in it and then secure it to the existing ceiling drywall (used 1/8" plywood for securing the screws into), mud, texture, put the can in (new or old work), paint and then the trim.