I've got vacuums a lot worse than those ones that never even left the house. lol They will need a complete teardown and a lot of cleaning, a lot of grease, a lot of polishing, but I wouldn't say they wouldn't run.
I have a Miele Salsa that was in a basement flood and the entire motor looks like the Titanic, but some electronics contact cleaner and a soft wire brush and a lot of scrubbing and she runs. Not well, but runs. Still needs more work. Polishing the little contacts with a tiny little dremel tool was the most laborious part.