Combining channels into single FFT left/right vs mid/side
Whether FFT(L+R) will work depends on how the stereo recording was mic'd and mixed.  

If just 2 separated stereo microphones were used to record a group of spatially separated sound sources (say an orchestra), then there will be location and frequency dependent phase differences between the 2 channels than could cause cancellations or nulls in a simple (L+R) mono mix.  If a lot of individually mic'd tracks were mixed down into 2 channels, this might be less of a problem.