Can lost water pressure cause a water heater to leak/rupture?
No, low water pressure would not cause the water heater to leak. BUT, there may have been a sever pressure SPIKE that caused the the leak that the water dept. crew was trying to fix, and that spike may have ALSO damaged your water heater. 

You might want to have a peek at all of your other fixtures and water based appliances too. For example your washing machine and dishwasher have cheap little plastic valves that turn on when you do a load, they may have burst as well. But in those cases the tubs will just fill and then drain out the waste lines, so you don't know there is a problem until you go to use them, by then you have run up a huge water and sewer bill.