If the Mac itself can run the OS, it should be able to boot from the copy of it.
I would *strongly* suggest getting an external SSD. 1TB is about $120 right now (
https://amzn.to/3sRekjy - affiliate link, so I'd get a teeny tiny kickback, but that's not why I suggest it) and 2TB is $199 (
https://amzn.to/3EMHToJ).