The way that line reads you know it does more for slow manumission than it does for expanding or continuing slavery. The only new slaves could come from the US and if the US was for ending slavery within its borders, at least that's what our northern history books tell us, there would be no more slaves coming in to the Confederacy.
Secondly, considering what was done at the draft riots and the position the north was in post-Gettysburg, would you go AWOL and with the consequences exhibited in NY to citizens, would you even want to?
That can't be true because the constitution forbids any law that might interfere with the institution of negro slavery. On the contrary, it was a means of protecting it by ensuring the supply of slaves from Virginia and North Carolina (which were not part of the confederacy when the constitution was adopted) would not be cut off.
...would you go AWOL
But they wouldn't have to, billbears. Their enlistments were up and they were free to go home if they wanted to. Unlike Davis who forced those enlisted to stay in the army, the majority of the Northern army could have called it quits and gone home. Instead the overwhelming majority reenlisted. Why would they do that if they didn't believe in their cause of preserving the Union?