Only if you bought it off Steam.
Actually, no. You can add non-steam games to your steam list as well. There's an "Add non-steam game" button in the games list that allows you to add non-steam games already registered on your machine to the Steam list. If the game doesn't show up in that list, then you can manually browse to the executable and add it to Steam that way. That's what I've done. I can launch all my games from within Steam.
Or, go your route which is add the games to the folder (including Steam games) and if it's a steam game, it will just launch steam first (if you don't already have it running, but I have Steam launch when Windows starts) and you're off and running!