You can. You can even close down Xbox and return to the same point in the flight. Last night, I pressed the menu button on the Xbox controller in mid-flight, then pressed the jewel button to get to power options, and shut down the console. This morning I booted up the console, opened FS (quick resume) and hit the menu button to return to the flight. It came back to the exact point at which I left it.
I am not sure how disruptive an update would be, however.