OT saints were indeed "born again" because they had the Spirit of the Lord dwelling in them (1 Peter 1:11).
To be honest I'm not sure about the language you're using? The OT saints may have been, in a sense, "reborn" if they had survived God's wrath and had become God's People, eg at Passover, and at the Red Sea, and also in the Wilderness. They, in a sense, "died" under God's wrath, and yet survived to live another, ie they were "reborn," as Jesus said. And Jesus said this while he was still under the Law in the OT era (Jesus was not, however, technically under the Law himself--he was not a sinner, and the Law was given for sinners).
But to say that the Spirit "dwelt in them" may be a bridge too far. In the NT sense, God's Spirit comes to dwell in us only under the New Covenant, because once we've been redeemed by the atoning death of Christ, we can live forever. As much as the Spirit may have been *with Israel* in the OT era, I don't believe they could say that the Spirit was permanently inhabiting people, because to permanently dwell in them implies that they have eternal life. And that couldn't happen until Christ provided his eternal atonement. Atonement under the Law was only temporary, and given to last until Christ came and provided a "better sacrifice."
I will agree, however, that in some sense the Spirit of God was *in* the saints of the OT era. He just wasn't in them on a *permanent basis,* because they had not yet been eternally redeemed. I can't see how a saint could be a saint, or even if a pagan could do something right, if the Spirit did not operate within them, speaking to their conscience. Even more, the saints walked regularly with God, indicating that in some sense at least God dwelt in them. So I'm just trying to make the biblical distinction, using biblical language, to avoid confusion.
Let's just say that the Spirit of God was "in the OT saints," but not fully "dwelling in them?" That's probably the best I can do right now. "Dwelling" seems to capture the sense of a permanent habitation, as opposed to just a "regularly habitation." OT was "regular," but not "permanent" yet.