The existing system opens each save game file in any case, to get the game time - the UI then translates the game time into a localised date / time for display to the user. Sorting by time adds no noticeable overhead. It seems to be sufficiently fast at present, I have 56 save game files present in the same folder.
So, I doubt checking a) if battlescape and b) what turn in the battle it is, would add any more overhead. Its more how to determine the values for a and b.