Nope. Not at all. Played UT3, Crysis, HL2, CoH, Spore, COD, FEAR2, WIC and many others without a glitch. I also had one 8800GT while I was playing in a 19" monitor and then when I upgraded to a 24" I added the second card willing to have the same performance of the 19" but now in a bigger screen. In a nutshell, this was what happened, except that in some games I got even better performance with the SLI in a 24" when compared to the single 8800GT in the 19" screen.
Just make sure that your PSU will handle the load, keep your drivers/games updated and make sure your new screen will have a resolution of 1680x1050 or higher... Just for testing when I run the SLI set up in my old monitor the benefit is not so nice when compared to the 24" monitor.
It's doing a such a nice job that I am having a very tough time in justifying an upgrade for now. Probably I will stick with it until something really revolutionary comes up (like a Dx11 card or something). And, even then I will still save one 8800GT just for Physx...
If you look the Tom's Buyers guide you will see that one of the top choices even for 1900x1200 is a pair of 9800GTX+ which, roughly, is what I have and you will have.