Is there any reason to believe that slavery would have been abolished eventually despite the arrival of Christianity?

I admit I'm no scholar on the topic of slavery in the Roman Empire, but I find it hard to believe that Christianity had much to do with its end: the New Testament is full of admonishments to slaves to behave themselves and obey their masters... Slavery was, I gather, just another thing to get through while waiting for the second coming.

Charles Bradlaugh on Christianity and slavery:

"Humanity's gain from unbelief"
http://www.infidels.org/library/historical/charles_bradlaugh/gain_from_unbelief.html

The problem with history is our complete inability to know with any measure of certainty what would have happened otherwise. Of course, it's also difficult to determine what happened BECAUSE of x instead of what merely COINCIDED with x.
As for the Christian interpretation of slavery as punishment, we get into the age old argument of predestination v. free will. Do we automatically accept every occurence as the will of G-d or do we consider that events are a function of human choices/decisions although not necessarily our own. I don't know if they are necessarily mutually exclusive. Perhaps some things are predestined while others are under our control. (For instance, kaballah says that ever person has been assigned a soul mate by G-d but that each person has the ability to accept/refuse the will of G-d concerning that soul mate.) I prefer free will and the Jewish concept of tikkun olam. If what is and what should be/what is right/what is just are different, then I must struggle to change what is.