I would, but more like run a rag or duster not go obsessive. Have the tub be clean, but no need to see yourself in it. Things go dirty just from moving in, but I'd think most people would appreciate being able to use everything and put stuff up right away without having to scrub stuff.
Granted I've always gone from rental to rental which people expect ridiculous cleaning standards in my experience.
Yeah, when we move into this house it was from an apartment and I spent 2 days scrubbing and cleaning after we moved everything out. We got our full deposit back too! I'm cleaning as I go, but I really don't feel like taking all the window screens off to clean the windows or clean all the corners with a toothbrush. I'm wiping out cabinets as I clear them out. I'd be embarrassed to leave the place coated in dust and gunk but does it have to sparkle?
Anna, I would just leave the house presentable and decent looking, not spotless. Like Jackie said the house will get dirty moving in and most likely the new people will do their own cleaning. Our house was filthy too, it was nasty. I always do a deep cleaning when we move in somewhere even if it looks clean. I want to make sure I "get rid of" the previous owners.