It wasn't like everyone wanted to get rid of slavery, and ornery Jefferson blocked it. The fact that a terrible war had to be fought over it should be good evidence for that.
There is experimental data here; France, from 1315 has prohibited slavery in mainland France, and moreover any slave setting foot on the soil of mainland France would be instantly freed, at least in the eyes of French law, from then on, and at the time, France was an absolute monarchy. The UK eliminated slavery in 1833, long before the US did, and they don't have a proper constitution to this day.
The fact that we were one of the last developed countries to eliminate slavery shows that our constitution did not hurry the day that slavery would be eliminated.
I personally wonder how necessary a constitution is for a functional republic; it is supposed to protect the rights of the minority, but I'm not sure the historical evidence comes out in that direction.
To more directly address the question, I honestly don't know. My first instinct is to exclude the south. Of course, that excludes most of the founders. But think of what an industrial powerhouse we would have had to become to survive, without the agricultural money. Would we have made it without them and the agricultural money, which mattered a lot more back then? would they have joined us in a more peaceful sort of way? Would we have ended up conquering them anyhow, and perhaps subjugating them in a way that ended up being better than what happened during our timeline, the appeasement in the name of unification? I don't know.
Some progress is better than no progress. It was called a "compromise", after all. The Constitution contained both the justification for emancipation, and the legal framework to enact it. The seeds were there, it was only a matter of time. The South saw that inevitability and seceded to try and avoid it.
If you have a theory about how it could have happened otherwise, I'd be interested to hear it.
Seriously. Jefferson wasn't a delegate at the constitutional convention. He was in France.