The answer for a lot of units is YES, ask how much leave is being carried forward, and why!
Techies usually manage a quick 'break' of 10 mins, whilst drinking coffee and filling in paperwork, which is not quite enough time to run down the gym and back.
Depending where you are in the techie food chain,
My heart bleeds and I am sure there is some truth in that statement. However, if the Chain of Command dictates that there is to be down time for phys, the over worked techies need not worry as,like true military personnel, they will do as they are told. The it is up to the their lords and masters to manage the roster etc and accept any reduction in output.
Having said that, studies have shown that people who take regular exercise and generally healthing in body and mind and able to cope with stress etc so there might not be any change in output as people wrok better?