fwiw I have absolutely transferred a live server from mains on to a UPS with a horrifying male-male hookup (and power-strip). It's possible, but still decidedly stupid.
(Stupid things I did at work because a: uptime, and b: I could)
hard drives don't like it, but if you're already prepping for such a "transition" you have the opportunity to reduce disk IO, maybe even park the disks
(In my move, the server was placed on a rolling cart and rolled so while yes there was vibration, it wasn't "big shakes" at least as though someone were carrying it (I wasn't about to touch it with a 10-foot pole while I transferred its power)
Or use SSDs!
lol that wasn't really an option for me in 2008 or so. Also, hot-swapping all the machine's drives to SSDs doesn't seem prudent or necessarily feasible.
(Depending on the ARP Metal hardware you're in, the hard drives aren't even hot-swappable to begin with)
yeah i'm not sure how much risk there is really from the hard-disk vibration
it also makes moving much more complicated though
especially when you have a lot of servers to move