If you want to use two cards in an Nvidia surround configuration, for the purpose of not dropping the frame rate, then you'd have to use them in SLI and these days SLI is pretty well dead. Certainly it's still out there and works, but the majority of devs don't create profiles for it anymore as single cards are powerful enough now to not have a need for it. So, results might be widely varied when using SLI on modern titles.
Yes, you should be able to use two 1080p monitors for a 3840x1080 surround configuration, as seen here:
However, you ARE going to lose frames, because with SLI, and you WILL have to use SLI if you want to leverage both cards performance for gaming, because with SLI the second card is going to lose some of it's capability due to the scaling effect of the configuration. Rather than getting double the performance you are probably going to get more like around 60% of the performance of the second card and since you are DOUBLING the number of pixels by adding a second monitor, you are likely to see something in the neighborhood of a 40% reduction in frame rates over running a single GTX 1080 with a single 1080p monitor.
So the bottom line here is that if FPS is your priority, you are better off with a single card on a single monitor. If the surround visuals are more important, then in general you will need to accept the fact that performance is going to take some kind of hit up to and including potentially as much as a 40% drop. Certainly, various settings for quality and the difficulty of the game title itself will dictate whether or not that is acceptable based on your preferences.
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