i like vyos a lot

yes, it will work - i have done exactly this (wired a pi to the 5v rail on a PSU) with no issues, but i used a 5v buck converter to regulate the voltage as i didnt trust the PSU fully. should be fine without a voltage regulator too though. but i would still rather use a 5v project power supply, you can get a 5v 20a power supply for $20 on amazon and wire every pi to it