Lol, and I thought the vibration concept was a new innovation from Mach 3 and Fusion. Guess not!
I would personally try one since I always preferred vibrating carts, but in this case I'd be afraid of getting electrocuted. Reminds me of a hairdryer in the bathtub.
It looks to be in excellent condition. I'd try it. I'd take a lamp in the bathroom, and plug it into a GFI outlet for safety's sake. And make sure someone's around with a fire extinguisher. And 911 on speed dial.
Given its appearance, it's probably fine. I used to fix and use fans and lights from the 20's that were a lot hinkier looking than that. I would recommend a GFI outlet be used, (for the lamp) at least initially.
How does it keep the water away from the electric parts? If it is by rubber, I would be afraid as the rubber is probably not in any good condition anymore.
The base plate could be one of those trough design with an open comb where the edges go upward (like the Merkur Progress). I have seen a couple of these on eBay and Etsy, but this looks in very good condition. Still, I would update my will and insurance policy before attempting a shave.