Crossfit to me is similar to P-90X except that Crossfit is more dependent upon heavy weights. Like P-90X, Crossfit should occasionally be used as a training tool for a "cycle", but you might not want to depend on it long term every month while you're training in martial arts. Again, you should primarily focus on the training that makes you better at the martial art you're studying. There will be "some overlap" between what you're doing in Crossfit and what you need to train in to be successful at your martial art.
Yes, all physical training that improves strength and stamina is beneficial however, why go to a price "gym" when you could accomplish the same at home with a few adjustable dumbbells, a chin up bar and an adjustable bench?
Sounds like your fitness regime is already worked out cross fit would be alright to stay in shape for ya summer triathlons you probably need something better then that but
NO!
Do you even lift bro?
So I'm doing triathlons / marathons during the warm seasons and martial arts during the winter as my main sports.
There's a nice crossfit gym just around the corner from where I live, it's kind of pricy. Should I give it a shot?