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.
So. To answer you "hypothetical" question if we ignore all the factors making it complicated (like 32bit compatibility, drivers, etc.)
Yes it is "feasible" to Install an OS using a modern System and just pull out the HDD and shove it into an old system. Especially since the way BIOS/MBR (aka "Legacy Boot") is the exact same on all systems you write the "what to start" code in the first few Bytes on the HDD (aka the MBR) and set a bootable flag on the device. Now you can pull it out and plug it into any other machine which will simply "look" for a bootable flag and then run the code in the MBR (usually a bootloader). This bootloader (usually grub for legacy systems) will then execute one of its boot entries and start a kernel. This is probably where a real world example fails because of the problems mentioned by everyone here.
Yes, thank you. I just wanted to make sure that was a thing. Thank you for actually answering my question.