I inherited a hot tub from my grandparents. I've drained it because the water was several years old (but he kept dumping bleach in - I know I'll have chemical issues). It's one of the very old marble-like octagonal tubs. It has a blister of sorts on the shell. It's about 6"x2" and projects out about an inch and it's right where one of the seats meets the wall. I don't see any cracks or leaks but it does look like the finish looks like a shattered windshield in that area. Should I run some of that stop-leak stuff through the system just to make sure? Does it need to be drained like a real blister? Is there anything I can do to make it look better?

No on all counts. That's just a bubble in the acrylic. The tub will probably hold water just fine even if that breaks thanks to the fiberglass / resin behind it. Anything you do to it will only draw more attention to it.