The short answer is no.
‘Hang on!’ I hear you cry. ‘Don’t you have to be regenerate to even come to believe?’ Of course, that is right. You do, indeed, need to be made regenerate before it is possible to believe, whether under the Old Covenant or the New. Dead people can’t will anything, after all.
‘So, do you believe there were two different means of salvation across the covenants?’ No. One was always saved by faith in the promised messiah. Faith in the promised messiah could only come about by a regenerative act of the Holy Spirit, whether under the Old Covenant or the New Covenant. God’s plan to unite a people to himself through his promised seed remained the same plan, across the covenants and ever after.
‘So you agree that the Spirit had to make people alive under the Old Covenant?’ Yes. Unless there is a work of God upon the heart of an individual, they cannot believe. That work of God is a regenerative work of the Holy Spirit.
‘So, you believe they were indwelt?’ Again, no.
‘But what about David? Didn’t he ask that God wouldn’t take his Spirit away from him?’ That’s right, he did.
‘So, David was indwelt?’ Not exactly. God’s Spirit, we are told, was ‘upon’ David; that’s the same Spirit David had seen not long before taken away from Saul. Saul also had the Spirit upon him as God’s anointed king but God’s Spirit was taken from him when David was anointed. Here, David asks God not to let the same thing happen to him. David had God’s Spirit upon him in his role as king, not dwelling in him (hence why there was a need for a tabernacle where God specially dwelt).
In fact, in the Old Testament, God’s Spirit was only ever ‘upon’ rather than ‘in’ people. Moreover, he was never on all believers, but on certain people. Typically, Prophets, Priests and Kings. He was also upon – less usually – the 70 elders appointed by Moses (who held specific office) and Bezalel, who constructed the temple. But it is clear that he was not upon all. In fact, Moses specifically says that he wished the Spirit was poured out upon all (Num 11:29) with the clear inference being that he wasn’t. The Spirit was only upon those appointed to certain offices and tasks.
‘So, how did anyone become believers then?’ As we’ve already said, they were made regenerate by the Spirit.
‘But doesn’t being made regenerate imply indwelling?’ No. Regeneration and indwelling are two separate things.
‘So, what’s the difference between regeneration and indwelling?’ Regeneration is the operation of the Holy Spirit upon an individual that imparts new life to them. It is the means by which God brings us to faith, the operation of the Holy Spirit upon our hearts, and the means of preserving God’s people. Indwelling is the seal of the Holy Spirit, the taking up of residence within our hearts by the Holy Spirit, affirming that God’s covenant presence is forever with his people.
‘But weren’t the Old Covenant believers also God’s covenant people? Wasn’t his covenant presence with them?’ Yes, it was. But it was set in the tabernacle and, later, the temple. God dwelt with his people in the tabernacle and then in the temple that was in their midst. The reason that nobody (save the high priest) could enter the holy of holies is because that is the place where God’s special presence dwelt. When Jesus died on the cross, the temple veil tore in two. No longer was man separated from God’s special covenant presence but God set his Holy Spirit – and thus his special covenant presence – in the hearts of those who believe. Should God’s special presence already have been resident in the hearts of those who believe by an indwelling Spirit, the temple would be null and void and the holy of holies of no consequence.
‘So, the Old Covenant believers had God’s covenant presence with them in the temple but New Covenant believers have God’s covenant presence in them through the indwelling presence of the Spirit?’ Yes. That is why throughout the Old Covenant, the Lord is said to be ‘with’ or ‘among’ his people whilst, in the New Covenant, he is said to be ‘in’ them. That is similarly why, when Jesus promised the Holy Spirit would come, he told his followers, ‘you know him, for he lives with you and will be in you’ (John 14:17). God’s covenant presence was with his people by the dwelling of the Holy Spirit in the temple but, following Jesus’ salvific cross-work, the Spirit took up residence in the hearts of believers making them the new temple.
This means Old Covenant believers were saved and preserved the same way as New Covenant believers; by a work of the Holy Spirit upon their heart that we call regeneration. But Old Covenant believers were not indwelt by the Spirit. God’s covenant presence rested in the temple and moved to the hearts of New Covenant believers following the cross.