Quote from the Archwiki (Installation guide):
Arch Linux should run on any x86_64-compatible machine with a minimum of 512 MiB RAM, though more memory is needed to boot the live system for installation. A basic installation should take less than 2 GiB of disk space.
Does that mean it is technically possible to get a Windows XP-era device with 512 Mb RAM and install Arch on it by pulling out the hard drive, connecting it to a modern machine via a SATA to usb connector, for example, with the modern machine running the live environment, and then just partitioning and installing on the old computer HDD, then putting the hdd back on the old computer? Is something like that feasible? I don't have a machine to test it on, but it certainly sounds like a fun experiment. It sort of reminds me of the stories of Gentoo cross-compiling.
Edit: It is a HYPOTHETICAL question. Please focus on the METHOD and IMPLEMENTATION instead of 32-bit compatibility or driver issues.
I don't know about Arch, because I've never used it, and I believe it only installs the drivers for the current hardware. I've done it with either Ubuntu or Mint though, and even with Windows XP and 7, though they were harder.
I haven't done it as a deliberate choice during installation, but I have had a working OS on a drive that I've then transferred to another computer. In the Linux cases, I've just put an old drive into another computer to see what would happen, as the drive was due to be wiped anyway. It was several years ago, probably over ten years, but for the most part, they just worked. The first boot was slow, presumably while the drivers were sorted out, but I think the most work I had to do was reboot a few times, after it got to the desktop.
With Windows, I had to delete a drivers folder, I think under C:\Windows\System32, and delete a registry entry. It didn't work every time, but it did work fairly regularly. It may have been down to the Windows version, home vs pro, but I can't remember.
Hope this helps ๐