You should be able to, without issue. I recently had a hard drive crash and had to completely reinstall Win 7 and all my programs. Obviously I couldn't deactivate either, and I have Photoshop on my desktop so both my license seats were taken. PS went right in, no problems. I'm guessing it knows what computer its on by the motherboard, like Windows does.
If you CS6 I believe that is what you mean by Photoshop. Which version did you have installed? The perpetual CS6 version 126.96.36.199 or the subscription version 13.1.2. If you had the subscription version there should be no problem. If the perpetual version if your activation credentials are still intact installing CS6 on top of CS6 I would think would install the perpetual version. In any case I think you best course of action would be to download the CS6 direct installer and install using that for the Creative Desktop application may thing CS6 is installed. Download CS6 products