Two combat missions on the scale of FreeSpace 2?
Sure. The average FS mission is relatively small-scale. People can stand a lot of strain. Look at modern "surge" style operations, or mid-late WW2 carrier ops. 9th Tactical's P-47 pilots flew an average of three ground-attack sorties a day for much of the Normandy period. You have to stand them down afterwards for crew recovery and craft maintaince, but you can maintain very high-tempo operations for several weeks.
Thus it's more likely FS consists of a series of short-duration, high-intensity combat sets, likely corresponding to the period just after your transfers between squadrons, with maintaince stand-downs and perhaps light patrol duty between them.