No, the vampire does not have a tracker for this. I think it might be something Lone Wolf might come back and address at some point - they own the Vampire coding. In the community files a lot of the authors work around this by adding a tracker so you can track on the in-play tab, see the demilich (which the community owns). The Tactical Console doesn't reset the trackers after the end of each round, so it still becomes a manual process anyway. I would like to see the tactical console update/decrease durations when you advance the round, but it doesn't.
If you think you want to see an official tracker in a future version of HL or other enhancements, you should open up a
bug report. This would put the request on LW's radar, as the devs sometimes are too busy to check the forums regularly.