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.
Way overcomplicating it, sure you could do that, or you could just Install arch using cdrom. it's worked on Windows 98 PCs it'll probably work on Windows XP PCs.
though you may need an older ISO to hit the 512mb limit