Tracing an Ancestor's Path through WWII

I realize this is probably a long-shot question, but I'm trying to trace the geographic path of an ancestor who served in the Army during WWII. He was, per family recollection, naturalized while serving in the military. The records we've found make clear that he was NOT a citizen when he enlisted in March of 1942, and the earliest he would have been eligible for naturalization would have been in May of 1942. There's some writings--though no proof--that his naturalization took place in 1942. I know that he could have been naturalized anywhere in there--and quite possibly wherever he might have been stationed before being shipped overseas in a federal or even state/county court, so his movements during this time period are the only way I have of narrowing an otherwise impossibly broad search. 

A request from NPRC for the full file came back with what we were told was the only mention of this ancestor in their records to survive to the fire: a pay stub that places him at Camp Davis, NC on April 21, 1943. It is a final pay roll for "6th Battery, A.A.S. (Artillery)", and on the page marked "Losses for March 1943" his name and serial number appear with the notation "Trfd to the 14th Battery". Family recollection is that he was in an anti-aircraft unit and served in Europe at some point during the war, though I have no idea when. 

I know next to nothing about military records or how to interpret them, but I had a few questions I'm hoping someone might be able answer:

1. If he enlisted in March of 1942, then he was still stateside almost a year later according to this pay stub. Is it a safe assumption that he likely was not deployed overseas in the interim? Or would it have been common to have been deployed to Europe, and then sent back to the US for further training within a year? 

2. If he was enlisted at Camp Grant in Illinois, did that mean he would have shipped out to basic training immediately, or did "enlistment" possibly mean he would have gone home for weeks/months before reporting to boot camp? 

3. Is there any way of trying to figure out where he might have come from-gone after Camp Davis in early 1943 based on transfer from a 6th Battery to the 14th Battery A.A.S.? I've tried google, but I can't make sense of the terminology or which batteries were dissolved and folded into others...

4. The NPRC said that in some cases the Veterans Affairs Department has military records in their custody, but offered few details. Has anyone had experience finding such records through the VA? 

I realize it's a tiny shred of information to go on, but would be grateful for anything someone can make of it, or insights into these basic military questions. 

Many Thanks!