Hello TrainNovice206
Yes, there is the SBB Travel Office on the same floor as the arrival hall. Just follow the signs to the train station.
https://www.sbb.ch/en/travel-information/stations/find-station/geneve-aeroport-station.html
Without knowing the travel time and departure, I am unable to tell you if the train will be busy or not. When you look up the connection, three human icons indicate how busy the public transport service will be.
A ticket, no matter which, does not guarantee a seat as our trains use the free seating approach. If you want to benefit from lower cost, you should purchase the Saver Day Pass as soon as practical. It gets more expensive the longer you wait, or there is a high chance that it is sold out at a given time.
Kind regards,
Roland