I can't lie; I never tried it. It definitely helps with an SSD, though. I couldn't imagine someone running an OS from a thumb drive. Which would probably surprise me and also work. Probably not as well.
Have you tested the data transfer speeds, maybe? Running a game or two? I'm curious. Will...
In a sense, you can. Since you already spent the money on the new SSD, just transfer your files over from the old drive to the new one. Then you can format the drive to be able to use it as a backup if you choose to keep it in the enclosure.