A movie camera is a work of precise mechanical engineering that doesn't really "date" if it is well-maintained. You can take amazing pictures on a 60 year-old 35mm Mitchell camera. If I took out the 65mm camera used to shoot "Lawrence of Arabia" over 40 years ago and put modern film stock in it, the images would blow away anything shot on a brand-new 35mm camera.
Assuming the movement of the camera is steady and in good working order, what really affects picture quality are the lenses and the film stocks used (as well as your skill in photography of course.)
What makes one camera different from another is more an issue of what features it offers; a Bolex, for example, is a very limiting camera for someone shooting sync-sound dialogue movies. It's not really designed for that. But if you want to shoot something that a Bolex is good at shooting, then the age is not an issue unless no one has been taking care of it.
My film school had a bunch of old Eclair NPR's from the 1960's and they took excellent pictures and were fine for sync-sound shooting; the biggest weakness was the quality of the lenses they had for the camera.
Now maybe if ALL your intended film school has is a couple of Bolexes, I'd be worried about how well-equipped they were. The age of the cameras are not so much the issue as the types of camera and the range of cameras. Hopefully the film school has some sync-sound cameras too, like some Arri-SR's for example.