I don't know if you are still looking for your father but I found this WWII record and it might be the right one. The age is about right. You could send for the military records and get more information.
U.S. World War II Army Enlistment Records, 1938-1946 Name: William F Allee Birth Year: 1922 Race: White, citizen (White) Nativity State or Country: Texas State: Texas County or City: Houston
Enlistment Date: 30 Dec 1942 Enlistment State: Texas Enlistment City: Houston Branch Code: Branch Immaterial - Warrant Officers, USA Grade Code: Private Term of Enlistment: Enlistment for the duration of the War or other emergency, plus six months, subject to the discretion of the President or otherwise according to law Component: Selectees (Enlisted Men) Source: Civil Life
Education: 4 years of high school Civil Occupation: Photolithographer Marital Status: Single, with dependents Height: 70 Weight: 124