Trivially on their (and qnap's) amd64 systems at least. There are some quirks where they are more similar to an embedded system than a PC, but it's not a big deal. Things like console over UART (unless you add a UART) and fan control not working out of the box, so you set it to full speed in bios or mess with config.

Debian has docs on installing on at least one model of their arm boxes: https://wiki.debian.org/InstallingDebianOn/Synology

I run Debian on a few different models of qnap because their hardware occupies a niche of compact enclosure, low noise, and many drives.

Why would you want to? That’s not what they’re for.

The kind of person who wants to do that is squarely outside their market. And you’d be paying a real premium for nothing.

I would never want to run a vendor OS on any device, they are either too proprietary or too untrustworthy or both.

Nope, the purpose of a Synology unit is to be about as complex as a toaster. Put it on the shelf, plug it in, make sure auto-updates are enabled, and forget about it until it sends you an email in 5-10 years that one or more drives is full/failing. I bought a synology almost 10 years ago and it's been purring away in a closet somewhere and never causing problems the entire time.

If you want a device to tinker with, this is the wrong product for you.

You cannot run a standard distro (easily) - their software (DSM) is linux based and they expose most of the stock services like Docker and libvirt