Boxing always complements striking well, however if you're that new to MT and want to compete only in MT for now I'd stick to more MT before cross-training until you have a decent level in MT.
Some of the best nak muay have cross-trained in boxing and managed to make that work in their MT or for Kickboxing, guys like Samart and Somrak. Even Buakaw when he transitioned to K-1 focused a lot more on his hands.
But they all already had a very good MT level before cross-training in western boxing. You don't want to spread your time across too many styles unless you compete in other sports than MT.
Also it's best if you do train more western boxing to do that within the same gym as they'll focus on what transfers over to MT instead of strictly western boxing competing which is very different in terms of stance, guard, focus etc.