The reason (I imagine) internet connection is required is to download the data files at game launch instead of having them local. This is what they did with the Elemental beta, and it means they can make certain changes (like xml fixes) without having to push out patches. When the game starts, instead of looking locally for the files it just downloads them from their server. This means that in theory, as long as your connection is available when you launch the game, it should work fine if the connection drops after. This is assuming that the data is downloaded once at game start, and not streamed continuously on a "as needed" basis.

As for how to make a copy:

Open your Explorer, and go to C:\Program Files\Stardock Games or C:\Program Files (x86)\Stardock Games. By default, I believe that's where Elemental installs. You should see the Elemental folder. Select it (click) and hit CTRL+C to copy. Go to another folder, or just go back out to C:\, and hit CTRL+V to paste. This will make a copy of 1.09 Elemental, which *should* work. Impulse will still start the game from the Program Files folder, to start the game from the copy you'd have to go to where you copied the game, and launch Elemental.exe yourself. You can also right-click Elemental.exe, select "Create shortcut", and then drag the "Shortcut to Elemental.exe" that will be created to your desktop, then rename it to something else, like "Elemental 1.09". Then you can use that to launch.

Hope that helps, don't hesitate to ask if something's confusing!