Hi! Welcome to the forums
If you're not installing ArtRage, but instead running it from an external drive and entering the key the first time you run it on a new computer, that key will remain on the computer when you're done.
Using it in this manner is fine on computers you own. However, if you do it on other computers, you could have your key stolen by someone else or someone could use ArtRage on that computer with your key which could invalidate the license, so I'd not recommend it.