Military radar in normal peacetime works the opposite way. Rather than controlling civilian airspace, it just monitors it, with a real-time data link to civilian ATC. On military monitors the known and identified targets are blanked out, so observers can focus on any unidentified targets. Thus military radar would not have monitored MH370, and if in the few seconds between loss of transponder signal and descent below observable height an unidentified blip would have appeared, that would have likely gone unnoticed. In all such cases it is a lengthy reconstruction process to retrieve the primary military radar data (which may first need to be 'weeded' to remove traces of any hush-hush activity), then match all targets with known and identified aircraft before anything may be said with any certainty.
I would not bet on this. One of the learnings of September 11, was for USAF to join the tactical and civil radar systems into one. Until Sept 11, US civil and military radar system were separated!
Swiss civil and military (tactical) radar is merged too. Civil or military ATC can initiate a scramble of F/A-18s.
And looks like Malaysian Air force seem to have more radar data than they currently disclose. All they say is that they are analyzing data.