No to your context, FDR had to go to a draft to fill the ground forces.
Enlistments weren’t cutting it.
That doesn’t explain him cutting off enlistments entirely.
Near as I can tell, WWII was the only US war in which voluntary enlistments were cut off. Civil War, Spanish-American War, WWI, Korea, Viet Nam all accepted both draftees and volunteers for the duration of the war. At no time during these wars was voluntary enlistment cut off. Again, enlistment was CUT OFF in Dec 1942. My context (regarding WWII) is precisely correct. WWII was fought primarily under the unique circumstances of neither the War Department nor the Navy Department accepting voluntary enlistment.
Again, this does not apply to WWI and SGT York.