You don't need to do road/mountain bike races to be competitive. However, at the beggining of the season you're road/mountain competitors will be still flying, and it'll take you a few races to find race fitness. As far as 'cross specific training goes, you need lots of threshold work (at least as long as you're race time) lots of vo2max work and some anaerobic work as well. Maybe also some slow speed standing-start sprints, as you do that often coming out of corners and off of obstacles. For running, once you can run 4 or so miles fairly easily, do some hill sprints, flat sprints, and maybe drills like "high-knees." Also don't forget a lot of technique work. And if you don't race until cross season, do something to test your fitness. (hard group rides, tt's, etc.)