I wouldn't swear to it, but I think what you describe is possible.
I've only been in the aircraft for one aborted start (because the T4 was getting a bit lively), and from memory there was no increment to the flight number.
However I bet I can guess your next question, and I'd lay odds that if there was an exceedence in that period then the flight would indeed be logged.
Good question though, one to put to Eurocopter I think.