One more thing to add--in the spirit of cross-training. (I've received excellent info from sports other than my own.)
When I trained for bicycle racing, I never, ever did any training that was exactly like competition. For say, a two-hour race, I would never do two hours at my max. I would do endurance training for two hours, but this was only at 65-70% of max. I would do interval training to work on my AT, but only for short bursts (30 sec to 2 min) with a good rest in between.
As far as training at maximum effort, some of the best advice was from Greg Lemond (the Tour de France winner) in his book: Don't train at your max when you are tired. When you train at your max, that is the closest to "the real thing". In the case of cycling, you want your body to be fresh so you can be going at top speed when you are at maximum effort. If you are tired, your maximum effort will not be top speed--you are just training your body to go slow.
If I was to apply this to grappling, then I think that grappling at max intensity when you are too tired will not be very productive. From the prespective of good technique and teaching your body to grapple well at max intensity, I suggest you should be fresh. I think that this could help in structuring a workout, but for class that is usually up to the whim of the instructor.
Just some stuff from left-field. I'd be interested in how well you think it applies in this situation.