I've been unable to tell whether time spent flying from location to location counts towards any of your own timers (research, construction, healing, etc.). That is, I've never had a project finish in midair or upon landing, even though some trips seem to take upwards of half a day. Does it affect any countdowns? It seems like it might still move time forward on alien actions, but I haven't noticed one way or the other.
(note that it at the very least affects achievements, assuming the "Exquisite Timing" achievement for beating it by July 1st works as described)
Best Answer
It appears that the internal timers are identical to the date/time representation shown on the geoscape: if time's passing on that, the timers are progressing.
However, not all timers are actively checked if the Avenger is airborne: project-completion and site-expiry events seem to only trigger while the game is on the Geoscape screen with the Avenger landed. Even if the timer for a project or mission site hits zero while the Avenger is in flight to a new location, nothing actually happens until after it has landed at the destination. Since landing at a mission site jumps you straight to the start-mission screen, this means that once you give the 'fly here' order for one things that would normally trigger in-flight are queued up until the next Geoscape visit after the mission ends (or until the player returns to the geoscape using a 'cancel deployment' option, which means such options should be used with care when dealing with time-sensitive missions).