Yes, that makes sense. Except the advanced notice should be as small as possible. Where I work the FAA has badges that let them walk right in, no signing in, no notification, no nothing. You always have to watch what you say and what you are doing because the feds could be in the cube next to you. Knowing when they are coming lets you get your act together and clean stuff up.
Back in the day when I worked hazardous waste we always know about inspections ahead of the time. So we cleaned everything up, labeled everything, got rid of stuff we weren't supposed to have, etc.
In both industries, almost all enforcement is after the fact. The FAA doesn't look over your should and say "Now use this drill bit, now use this primer, etc" they find out that you screwed up 5 months later during an audit and then they fine the hell out of you.
Once in a great awhile there will be real time enforcement of regs, but that is not the norm and would be impossible to do for even every very important regulation. That is what inspections and audits are for, it just so happens that when there is an accident it ensures an immediate inspection/audit/investigation. And then everyone whines that there was no real time enforcement of whichever regulation.