A fair point.
However, the Union forces did get vast numbers of black recruits, many slaves did run away or otherwise "self-liberate," etc.
(Plus there's an interesting little anecdote involving blacks from occupied St. Simons fending off Confederate raiders--one Confederate said if one wanted to go to hell before one's time, one should go to St. Simons and be hunted by N-words.)
A U.S. advance into British Southern America might get bigger and bigger as it moves south and accumulates more runaway slaves (as soldiers and camp followers) rather than attriting due to enemy attack.
The armies could be so swollen by runaway slaves that the British might decide it would be better to make a good peace rather than try to fight such a horde.
Also, if enough slaves run away, places like South Carolina could shut down entirely.
Furthermore, if the slave-white ratio gets really lopsided and the whites get really nasty in order to maintain their power, the slaves might revolt rather than simply run away or try to "renegotiate" their positions--they'd be angrier.
(Compare Santo Domingo to the antebellum South, frex.)
Well, to some degree this might happen, although in all likelihood not at the degree necessary to cause collapse of Southern society and US conquest of BSA. Britain would make peace well before that. This butterfly might however be used to justify the USA getting a particularly favorable peace (e.g. the USA getting all of Louisiana, New Orleans, and the right bank of the Mississippi).
I'm still doubtful that it would a be a major effect, for various reasons:
-It likely requires the slave-ratio in the BSA slave-white ratio to become so lopsided as in French Hispaniola, and I doubt that even with the slaves sold by the USA to the BSA when the former abolishes slavery, the BSA would reach that level of imbalance in the early 1800s.
-It requires a level of ideological committment to abolitionism on the USA's part which I dunno if it would be there: sure, it would have recently abolished slavery, in a relatively painless way, but just for this reason, I dunno if they would be that much committed to "export emancipation" as they were in 1863-65. After all, the USA disposed of its own slaves by selling them to the BSA.
-Dunno if runaway slaves would be that good recruits for the US forces. Enthusiastic, certainly, but trained and disciplined ?
All in all, it is to be expected that US armies invading the BSA would attact a sizable amount of runaway slaves as camp followers, and it may or may not destabilize, or threaten to, BSA society enough to be a significant factor in pushing Britain to make an unfavourable peace. But I doubt it would be substantial enough to collapse slavery in, or allow US conquest of, the BSA.
If the US armies accumulate significant number of these runaway slaves, what would be their future after the peace ? In all likelihood, neither the USA nor the BSA would be willing to welcome them. So I expect they would be trasferred either Hispaniola or to Liberia.