Are two colors (red + blue) necessary for LED grow lights, or would either color be sufficient?
tl;dr: Sort of?

Logically, either red or blue light should be sufficient. Chlorophyll a and chlorophyll b preferentially activate different photosystems, and both photosystems are required in green plants. 

Practically, we're in luck and someone has actually done the experiment.

As the original study reports, plants need a little blue light to grow into the right shape. Red-only plants produce oxygen and grow, but they take weird shapes. It seems like plants can grow on red light, but they use blue light to work out where light is. See here for a reasonably lengthy treatment on most of the obvious combinations.