Good 'private' chefs will, but as a chef who has worked in a commercial/restaurant kitchen....
I can tell you that any domestic cooking/cleaning skills you may have had, if any, go right out the window!
It took me a very long time after leaving the kitchens to return to cleaning as you go and being extra careful about my kitchen...
In a professional kitchen you simply don't have time to tidy up, your bowls, pots, pans, implements all stack up on your workstation and then "whoosh" a kp comes through and takes them away to wash - you just don't have time during a busy prep/service to take them over yourself...
Then you go for a ciggie break (or whatever break) and "whoosh" the floor has been mopped, because it has to be, several times throughout service otherwise the health department comes down on your kitchen -
So by the end of service you basically wash down your stainless steel worktable with a soapy sponge, dry it off, and you're outta there, leaving the kps to finish off the clean-up.
So try and picture how that translates to home cooking! It takes a while to sink in again that there is no kp at your service! And this is assuming that the chef has ctually had a lot of experience cooking in a home environment, a lot of chefs go to work in a commercial kitchen directly out of school, very young, having not cooked in a home designer kitchen with lovely wood floors and granite counters...
So, what I suggest, if you do want to hire a prof chef to work in your kitchen, also hire a cleaner/butler for the night, someone that will chase after the chef and mop up dangerous spills right away!