I think Tim Hegg damages the effectiveness of his argument quite severely when he uses his analysis of the "ger" in ancient Israel to make a point about the covenantal/legal status of non-Jewish Believers under the New Covenant. The ger is only relevant for our purposes if it can be shown that the ger was initiated into the Sinaitic Covenant by faith as opposed to circumcision. But Hegg's analysis is unable to do this as it contains several contradictions.
First, Hegg says throughout his writings that the term "ger" is not a religious term but rather a sociological term:
"…originally the word [ger] was a sociological term [and only] in the rabbinic literature it has become…religious…" (Fellow Heirs)
"While the word ger always bears a sociological meaning in the Tanakh, there came a time when the sages began to understand it in a religious sense," (It Has Been Said, Vol. 4)
"Kuhn has shown that the meaning of ger and its Greek equivalent, proselutes, moved from its original sociological meaning to a purely religious, technical term in the late Second Temple period. Whereas originally the terms simply identified a foreigner who had taken up residence in Israel (without being specific about his relationship to Israel's God and Torah), by the 2nd Century BCE the words were being used more and more to denote a convert to Judaism," (Is the Torah Only for Jews?)
"When the context makes it clear that the ger has indeed attached himself to the God of Israel, it is often plainly stated that the ger and the native-born have the same privileges and responsibilities as covenant members," (It Has Been Said, Vol 4)
"Leviticus 17:15 begins with 'any person' (v'kol nefesh) and further adds 'whether native or alien' (ba'ezrach uvager), showing that in this text the Torah was considered universal for all within the community of Israel. In contrast, the Deuteronomy passage allows the torn meat to be given to the 'alien who is in your town (literally, 'gates')' (lager asher bish'arecha), presumably because the alien (in this case) is allowed to eat what is unclean."