What you can do is trigger a campaign save from the cockpit, exit the airplane handing it back over to the AI. And next time load that campaign save and steal that airplane mid-flight from the AI. It won’t be exactly how you left it but largely the same (position, weapons). Falcon’s pretty unique in that you can take off, hand the plane back to the AI, wait until just before the target and jump back in. In fact you could be flying a strike, encounter MiGs, exit and switch to the escort flight, fight, and return to the strike flight and continue to the target.
I’m sure it wouldn’t be satisfactory for ground ops though as the inexactness of resuming would be quite severe in this case.
A quick errand I’d use pause though.