He did serve overseas!
Here is the record for his Silver War Badge:
http://search.ancestry.co.uk/iexec?h...src=&pid=25705
56967
Gunner
Hamilton, John
6B Res Bde
Enlisted: 26 Dec 1914
Discharged: 3 Dec 1917
Reason for discharge: sickness
Age: 23
Whether served overseas: Yes