Both of those will have worse performance, but I don’t see why they wouldn’t work. Just whenever it needs to grab more data it’ll have to go to the USB to get it, which is slow. You could load the game that’s stored on the disk already (this will require more effort and knowledge than installing Steam and it installing it locally on your Linux drive), so that’d be better, but the system data will be slow. If you have a lot of RAM it’ll reduce how often data is grabbed, so it’ll reduce the issues after boot.
Both of those will have worse performance, but I don’t see why they wouldn’t work. Just whenever it needs to grab more data it’ll have to go to the USB to get it, which is slow. You could load the game that’s stored on the disk already (this will require more effort and knowledge than installing Steam and it installing it locally on your Linux drive), so that’d be better, but the system data will be slow. If you have a lot of RAM it’ll reduce how often data is grabbed, so it’ll reduce the issues after boot.