Fair enough. And I'll be honest - I'll have to look for sources. For the moment. given the conceded high level of straggling in the ANV while in hostile territory, I have a very difficult time believing that the straggling wasn't noted by observers. If ANV assessments of the level are correct, where were all of these guys hiding, what were they eating, etc. And there weren't likely all being secreted by the residents - this was the "Union" part of Maryland.
My understanding is that most of the stragglers can be divided into these categories:
1) Stragglers who fell out in Jackson's "corps" (Jackson Early AP Hill) or in McLaws' "corps" (McLaws Anderson) south of the Potomac.
These men would either have caught up with their unit a day or so later (before Antietam) or a few days later (after Antietam, joining the wagon trains which were moving over Boteler's Ford) and either way would have been out of contact with the supply system for only a couple of days. The area was not under Union observation and they would have had just missed a meal or two (at most; if they'd been issued three days' rations before falling out they might have had enough to eat anyway).
2) Stragglers who fell out in the movement from South Mountain to Antietam.
These men would have either rejoined the Confederate army or been swept up by the pursuing Federal advance guard; there were a lot of prisoners in the Maryland Campaign by some reports (references to several thousand unwounded prisoners being exchanged in the following weeks can be found; it's possible these were battle captures but it's also possible they got swept up.)
These men would have been noticed by Federal observation by being captured, and would have eaten rations in prison.
3) Stragglers who were disassociated with their units behind Confederate lines.
These men would have been part of the moving body of the Confederate armies but just not actually present with the fighting front at Antietam itself. In common with the stragglers who fell out south of the Potomac these men wouldn't have been observed; they'd have missed a day or two's rations if they didn't show up for food.
4) Stragglers who fell out in Maryland before the Confederate army reached South Mountain.
These men would have been amenable to observation, and were largely not seen.
5) Stragglers who refused to cross the Potomac and fell out in Virginia.
These men would also have been amenable to observation. Reports indicating perhaps a couple of thousand exist, but they can't really support ~20,000 or so (as would be needed to be the primary reason reconciling Lee's post-Antietam reports of ~60,000 men with his army hold up with the ~40,000 effectives he claimed at Antietam; if they're the
only reason then it implies the staggering total of 37,000 men didn't cross the Potomac, which is utterly untenable as it's almost exactly half of Lee's army).
My estimate of Confederate effective strength at Antietam is about 47,000 (having gone through the regiments/brigades/divisions) and this implies that there were about 28,000 men who did not fight at Antietam for one reason or another; of these many must have been just behind the lines because Lee's post-Antietam reports (September 22, plus the earliest returns for the artillery and cavalry) and adding-back a Maryland Campaign casualty estimate gives about 60,000 men.
Thus:
Approx. 75,500 (entered Maryland)
HF casualties 300
Cramptons Gap casualties 900
South Mountain casualties 2700
Not at Antietam: Thomas' brigade (about 1,600)
At Antietam itself: about 47,000
Implies 23,000 CS stragglers
Union captures unwounded about 3,200
Approx. 75,500 (entered Maryland)
Total Maryland Campaign casualties ~17,000 (so strength should be down to 58,500)
September 22nd state plus cav and artillery 43,000 (while units still disrupted)
Implies 15,500 men had not yet returned to the ranks by the 22nd
Approx. 75,500 (entered Maryland)
Total Maryland Campaign casualties ~17,000
September 30th state 58,500
Implies all stragglers have come back in by the 30th September, or rather that the number of outstanding stragglers is equal to the number of men who have recovered.
Approx. 75,500 (entered Maryland)
Total Maryland Campaign casualties ~17,000
October 10th state 64,000
Implies that large numbers of wounded have been recovering by this point, or possibly that men are being moved from extra duty to PFD categories to replenish the army's fighting strength. If this was already going on by 30 September it influences the numbers there by a couple of thousand (which would imply a couple of thousand stragglers who had not yet come back in).
This is consistent with the idea that most of the stragglers were not stragglers for a long time.
One model is that there were about 13,000 stragglers south of the river on the forced-marches to concentrate at Antietam, most of them from Jackson and McLaws' corps.
Notably my estimate for McLaws and Anderson at Antietam is about 8,000 between them and on 2nd September McLaws alone disposed of 7,340 infantry and 419 gunners; Anderson disposed of about 5,700 men. Anderson's division may have been disrupted when this return was taken, as in the October 10 return Anderson gives 7,800 PFD and McLaws gives 7,100; adding the 3,500 or so casualties they suffered in the campaign means that their campaign-start strength could have been north of 18,000 between them.
Heavy straggling in these two divisions would explain a lot of the estimated stragglers south of the river.
The rest of the stragglers in this model would be men who fell out of line and got captured by the Union (about 3,000) and men who were with the army but not with their units (about 7,000).
An alternative model is that many of those 13,000 stragglers in the first grouping did in fact try and catch up with their units and merely manage to catch up with the army, and were either with the wagon trains south of the river or "behind the lines" north of the river (to go with the ~7,000 the first model categorized that way).
If the idea of 13,000 or 23,000 stragglers sounds preposterous, taking the straggling recorded in 1st Corps of the Union army (about 30% or so of headline PFD strength) and applying it pro-rata to the whole Union force at Antietam on the 17th produces about 25,000 stragglers. Many of these would have fallen out of line on the march; the rest would be with the army but not with their units.