My understanding is this:-
1. The US citizen part is neither here nor there. As long as a non EU driver passes an EU driving test he is qulaified to drive in the EU.
2. The military part of the story could alter things a little as the minimum age for taking a test is 21 but in the military that can be 18, although for practical reasons the individual would have had to have signed up for a period of service to end beyond his 21st b'day.
3. The type of licence will be in two parts. The category of vehicle itself - in this case it seems to be a Large Goods Vehicle (LGV) which is a goods vehicle exceeding 7.5 tonnes. Secondly the type of transmission will decide if the driver is fully licensed as appropriate. That is to say a manual test gives manual and automatic i.e. clutchless, but an automatic does not allow a manual to be driven as a full licence.
Therefore the answer is no.