Jen,
Depends on a number of factors. Service and aircraft type being the big ones. I can talk to the RAAF only and the answer is you are a Pilot first and an "Officer" second (In my opinion). What I mean by that is when you first arrive at the SQN as a junior PLTOFF/FLGOFF your job is to fly, you will have basically no leadership role. As you progress through your career you will get more and more responsibility. Starting with progressing through as a Captain in your first tour on heavies or progressing as a 2 ship and then 4 ship lead on Fighters. The leadership role is not in it's typical sense though, as a Captain/2 or 4 ship lead you will make airborne decisions and direct other crew/formation members but that tis about the extent of it.
After ~10 years in you will look at promotion to SQNLDR where you will pick up a flight commander then XO gig, this is where the leadership role in its typical sense begins.
As far as other Officer related duties go there is a few that you will always be doing, promotion courses etc.
The above is the truth of it but I would suggest that recruiting would like to hear you say that you are willing to take on the role of an officer etc. etc. I.e Officer first, Pilot second.
Hope this helps, good luck everyone.