They do have something called Permatex The Right Stuff, which requires no cure time. But it didnt specifically list differential covers as a use.
I'd be with good finger tightening the bolts, letting it set for an hour, then tightening to spec and waiting a few hours to fill with fluid. I'm sure I could find a few things to help my parents with around the house while this sets up. The 24 hours just seemed excessive!!