This argument is invalid as stated. I think it goes something like this:

1. If a person has been given the Spirit by Christ, they are a member of Christ's Church.

2. The Gentile believers were given the Spirit by Christ like the Jewish believers.

3. Therefore, the Gentiles were members of Christ's Church.

4. Therefore, anyone today who "calls out to God as to their Father" and "lives in righteousness and puts to death the deeds of the flesh" is a member of Christ's Church.

As you can see, the conclusion jumps from being given the Spirit to calling out to God as Father and living in righteousness and putting to death the deeds of the flesh as the standard for being in the Church.

As stated this argument is invalid and seems to me to beg the question. In my thinking, the question of who is in the one true Church is precisely a question of who has been given the Holy Spirit. In order for this argument to be valid, a premise needs to be added that calling out to God as Father and living righteously and morally is sufficient evidence for one having received the Spirit. Even if this premise were added, I would argue that one could seem to call upon God as Father and live righeously and put to death the deeds of the flesh but still not have the Spirit.

To summarize: What needs asked and answered is how the apostles thought one knew that a person had received the Holy Spirit before we can settle the issue of who exactly is in the one true Church.