I am training for the World Championships in Full Contact Stick Fighting in a couple weeks and as a personal experiment have adopted crossfit as a regular part of my training for 2 months now. I do find that if you go to a fma school that pays particular attention to metcon and "cardio" training then doing Crossfit right before training can be detrimental to your stick fighting performance. I've done Fran and Cindy and a couple other WODs right before stick fighting which means then my Crossfit WOD>30 20 minutes jump rope> 30 minutes stick bagword> 15 Minutes footwork> 20-30 minutes stick fighting and drilling. With a WOD as an appetizer, by the time I'm ready to bang sticks, my arms are putty. Now I do the WOD in the morning or after my workout and I can see the impact that CF has on my fight game (more power, moresprint endurance, speed, etc). In fact, it is a wish for me to do well in the Worlds as a representative of the Crossfit community. If you are talking about a regular FMA curriculum class (90% technique) then I think that CF anytime before or after would be great.
One thing we like to do now in stick training are tabatas with sprints on the heavy bag and also burpees, sprawls, slam balls, tuck unders, etc. That is a great workout for fight conditioining imo.