I am not a military pilot, but generally in the civil world, flight plans are always filed if the flight will be IFR. That includes any flight above FL 180 regardless of the weather conditions.
A VFR flight may or may not have a filed flight plan at the pilot's discretion, with the exception being in the national border areas, where it's required. Being that most mil aircraft very easily break that FL 180 ceiling or travel a long distance, they are likely to file a plan.
In my experience, ATC usually can tell you if a MOA or other military airspace is active based upon the time of day, but unless a particular aircraft is talking to the controller, their info is limited to whether a route or area is active or not.
ATC is responsible for providing radar service (traffic separation and other services). It doesn't matter whether the aircraft is going 60 knots or 600, I don't believe that a military aircraft is required to file a flight plan unless the above conditions are met......