There is a midrash which states that Avraham "converted" people -- here is a retelling of it from another website
"'And the people that they made in Haran.' Rabbi Elazar ben Zimra said [the text should read] ...”these are the converts that they converted.” And if it is that they converted them, why does it say “make”? Only to teach you that all those who bring a worshipper of stars [i.e. a pagan] close [to God] and converts him, it is as if [the one who converts the other] created [the one who converts]" (Genesis Rabbah 39:14).
If that is the case, then convincing them of belief in the monotheistic god and their choice to follow Abraham helped them enter into some important status. However, only those in Abe's "family" were ushered into the covenant. Whether there was another step beyond belief (which would bring someone into Noachide status) -- such as circumcision (which would make the person part of the family) is not attested to by text as far as I know.