Not sure if it, or a similiar strategy/thinking game, needs to or should be added to any MA syllabus as such. But I do think that activities outside of the core MA training time or at the club do benefit your MA ability, such as chess from a mental perspective, or on the physical side, running, conditioning, working on flexibility and reflexes etc. I do think that mental agility and strategy is only a good thing for any fighter and that a game such as chess can improve ones thinking patterns in that repsect. Smart/strategic and tallented (physically) fighters often do better long term over just tallented ones.
I play when I can but am not that good, used to be average, maybe bit more, for my group back in high school when played quite a bit. I taught my girl (who played the Chinese chess equivalent and some other ancient war based Chinese game) how to play chess and after about the fifth game she was able to regularly beat me.