Most assignments (or at least the ones I receive at Meadowvale Secondary) are either in-class (which means even if you wanted to work on them at home, you couldn't), or are due in a few classes meaning you'd have nearly a week to finish it. Other paper homework can be completed the day it's assigned. Again, this is from my experience in high school (I'll be in grade 11 on September 7), whether it works this way across Ontario or the Country I don't know, this is just how it works with me.
Besides if your BMQ will be being done every other weekend (or every weekend depending on a situation you may find yourself in, such as Sig Op's) then that means you still have 5 days beforehand to complete all homework / assignments, maybe even some time to review...and depending on which day you are assigned these things (and seeing as how it's high school) I don't see why completing homework before the weekend would be a problem.
As for teachers understanding this kind of situation, yes, some will give exceptions, others will say it's your responsibility to complete homework assigned for the day it's due for, since joining the Army was your choice. This was the case with my English teacher last year...I had a 3 day hockey tournament which means I missed a Friday on which an essay was due. I was told that I would have no extension and would have to hand it in a class early. I know hockey and military aren't the same thing, but my point is some teachers will not make exceptions.
AGAIN...this is with my experience.