There is no overarching list of what weapons were assigned to what units. Remington Ilion produced 545,541 M 1917's with the highest serial number being 647358 so your serial number is near the end of their production run if you have an Ilion. Remington Eddystone produced 1,181,908 rifles with the highest serial number being 1332477.
This site U.S. Rifle Modle of 1903 (m1903.com) has information on the M1917 and does have a place to ask questions.
They have a listing of where the markings are located for either Remington Eddystone or Remington Ilion here:
In my copy of the Springfield research guide the closest I found to your serial number was a Remington Eddystone serial number 636871 which was used in a firing test on October 24, 1918.
The 1917 saw service in WWI and WWII.
Texas Military Forces Museum