It is entirely possible for a man to have served in the army in WW1 and left no offical trace. The most comprehesive records of service are the medal rolls- but these only cover men who entered a theatre of war. If a man was not an officer and served only in the UK (no medal roll entry), survived the war (no CWGC or Soldiers' Effect entry), remained fit (no SWB or pension record), and his records went up in smoke in 1940 (no service record) then you are very unlikely to find any army record that proves he served. I suspect this applies to many thousands of men.
However, you might find them mentioned in a local paper or the 1918 electoral roll (either in special Absent Voters List or marked 'NM' in the main roll).