It may have a minor effect on your FPS. What you are asking is no longer a simple "A + B = C" question. Some of these factors are: what is happening on the second screen, what version of windows, how much memory does your video card have, how much memory (video and system) does the program need? This is not a complete list, there are many other factors that will effect this new equation. If the video is "being delivered" by the video card, it doesn't matter if the screen is on or not. Kind of like purchasing Pay-Per-View on cable/satellite, they are going to charge your credit card whether you watched it or not.
If you must know a definitive answer, use FRAPs to do a FPS capture with the second monitor connected, and then again without the second monitor connected. Make sure you do at least 5 runs doing the same thing for each test. Make a save point then run from point A to point B following the same path each time. Then you will have a clear answer to your question, "Does having a second monitor connected to my computer make a noticeable difference in playing <name of your game>?"
To sum it up (pardon the verbose answer), if the second screen is not blank there will be an impact on the system. How much of an impact? I highly doubt that the impact is significant or noticeable.