Is there a way for the competition controller, or anything else for that matter, to tell a cortex or V5 controller how much time there is left in a match?
You mean field control to communicate with a robot? No, not currently other than to enable and disable/trigger driver or autonomous mode.
Its not ideal, but could you start a timer in the driver controlled program right at the beginning? I"m guessing you want to perform something automatically at a certain point in time, or make an alert of some form (lights, etc) at a certain time of the competition? This might get you close enough.