I'm going to say yes, unless someone has a definitive ruling to the contrary.
https://swmgamers.com/SWM/Rules/StartProcedures.pdfWith Master Tactician, both players roll initiative as normal and those initiative checks are used, for example, to determine Reserves. It's just that with MT, the MT player just gets to win automatically - ignoring the rolls. That is, unless MT faces MT, in which case the rolls (including Tactician) would come into play.
I was the one who put that guide together, and while I don't recall thinking about that interaction specifically, I was pretty meticulous about making sure that document lined up with every known ruling I could find.