Answer
Lutherans and Roman Catholics believe that salvation, in some form, always accompanies baptism. But it sounds like you are describing the doctrine of presumptive regeneration, which is held by some Presbyterians and others. Essentially, the doctrine holds that we should assume the best about those who are baptized, trusting that they are elect unless they prove otherwise. I agree that this doctrine does not have sufficient biblical warrant. However, it is not the only view among paedobaptists.
Believers who do not come from a covenant family receive exactly the same salvation as those who do. Yes, they miss out on the benefits of the covenant before they come to faith (there are benefits to being in covenant with God even if you are not saved; see
Does God Love Everyone?). But once they come to faith, they are part of the covenant. The easiest way to see this is to look at all of Paul's arguments about the Gentile converts being equal Christians with the Jewish converts (e.g., Eph. 2).
Because our salvation is "in Christ," we are stand before God as if we were Christ himself. As a result, we all have the same status, the same privileges, etc. Our eternal rewards may vary according to our works (see
Different Workers, Same Wages?), but we gain no eternal blessings by virtue of our covenant status at birth (cf. Phil. 3:4-7).
Finally, the promises given to Abraham were conditional and two-sided. If one is in Christ, he is counted as a covenant keeper and he receives the blessings promised to Abraham. If he is not in Christ, a person's sin places him under the curses promised to Abraham. So, it is safe to say that everyone in covenant with God will receive the promises, and this is because God is faithful to his covenant. The bad news is that if you are reprobate, those promises are curses.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.