Nobody'll really be able to tell you if it's stable 7 minutes in unless it has some sort of error (in which case, no). If there's no errors 2 hours in, it might be stable. 12, it probably is. 24 hours though is what you'd want to be error-free for in stability testing.
If you're just testing the waters, making sure your OC isn't going to catastrophically fail, I don't see any real harm in running prime for 30 minutes to an hour before bumping it up a little (as 4.0 is a little low compared to the 4.6 or 4.7 most people achieve on air).
Right on. I guess that means you're not looking to push it higher than 4.0? In that case, yeah, you're going to want to run prime overnight to ensure it's stable. It can seem just fine even 12 hours in, but there's no guarantee it won't fail even then.