I feel that you would have to dictate the pace of the matches and keep them slow to make a strength increase really benefit your conditioning. if there's a lot of explosive, agility type transitions and an overall fast pace, then i feel that your conditioning will not improve as much focusing on ME strength. if you can crush the guy in side control for several minutes or keep him broken down in a tight, closed guard for a long time, then maybe you can keep a steady pace that will be improved with some brute strength. i do know guys who roll like this. granted, these are in class, and not in competition.
on the other hand, it does not make sense to believe that you can rely on anaerobic strength for 100 minutes (10x10min matches). granted, these are broken up by rest periods, but a large majority of you energy will be provided through aerobic means.
just doing a brief search, it looks like a strong half marathon time is 80 minutes or below. that's around an average rate of 10mph. the world record is 58:23, a rate of 13.5 mph. those guys are able to keep that kind of pace by training predominantly aerobically. i'm not saying you need to become that kind of dude, but you can rely on your aerobic capabilities to keep a good pace in your matches.