Pamphlet on "Naturalization Certificates" for soldiers being discharged following WW1.

"Soldiers who are aliens may be naturalized before being discharged from the army. If they desire to do so, they should notify the U. S. Army Naturalization Officer immediately upon their arrival in Camp."
From- "For Discharged Soldiers of the United States Army WW1" compiled under the direction of Major General W. A. Holbrook U. S. Army, commanding Camp Grant, Illinois." April 25, 1919.
Further details in General Orders No. 146.

The above from http://freepages.genealogy.rootsweb.ancestry.com

Army recruiters at the time of WW1 would accept aliens who wished to serve and were physically able to do so. How they entered the country was not asked.