In BGE I can use Matcap when viewing objects, but when I press play and play the game can I use Matcap? It's real-time, so I can't see why not... That would give gameplay great graphics if I'm correct.
Matcaps are a viewport shading feature that doesn't exist in the game engine. Note that matcaps are applied the same to every object in the scene which is normally not what you want in a game.
You can however use the matcap images used by blender (or from other sources) in your textures which can then be used in the game engine. This question shows the settings needed for both Blender Internal and Cycles.