Sure - you can do that. Unless you have the license server version (doesn't sound like you do), you can install Slickedit however you like. The restriction is that you're only allowed to use it on one computer at a time.
When you do the product download, you should see a button for "generate license file". That's your ticket right there.
For instance, I have it installed on my computer at home, on my computer at work, and on a laptop I use frequently. I only ever use it on one computer at a time. Fully within the rules set forth in the license. My work computer is "new" as my old computer died about a month ago. One of the first things I did was download VS and install it on the new PC. I can't seem to do without it.
(And someone from SlickEdit may chime in. I don't think I'm wrong.)