I did it with one of my games exactly as you say just to see what would happen. I did the "trial" with one of the smaller downloads so if I would have to redownload, it wouldn't be a huge one. But when I dragged and dropped the file from the exterior drive back into the Program Files (x86) file (which is where Windows 7 puts them), I double clicked on the execution file and the game opened right up. After I played for a bit, I closed the game and the game manager appeared as usual.
Try it first with one of your smaller games and see how it goes.
You may be able to play them right from the exterior drive too, like MaG does. I don't know if the game manager needs to know where it is. I don't use the game manager, but rather shortcut icons to play my BF games.
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