As for pushball, one of the brawls was my flight vs another one. Yeah, pushing wasn't the only thing that went on in that game...
As for MTB's, it really depends on the injury, recovery time, whether or not near-full recovery is a great possibility, ect. Two people in my flight got stress-fractures, and the first one got it at the beginning of Jack's Valley. Although she was unable to do any of the courses because she was on crutches, nothing else happened. So, there are a couple of different factores to consider during Beast. After Acceptance, as long as you can get to your classes without too many absences, and you will recover at least sometime relatively soon (no more than a couple of months maybe?) I think you won't get a MTB. At least, that's how it was explained to me. Pretty much, don't do pushball or do anything stupid, and you SHOULD be ok. Weird things do happen here though, so you can never be sure.