Some flights do stop in Shannon en route to/from Europe but sometimes you may not be allowed to deplane (except for a secure part of the terminal for in-transit passengers) - depends on the mission. Some passengers on USN flights have had some luck manifesting to Shannon (but it's rare). If the flight is going to RON at Shannon then Crew and Pax will have to clear Republic of Ireland's Immigration and Customs. Getting a flight from Shannon would be fairly difficult.
Can I fly Space-A to Shannon Ireland?