A person can be born again without abiding…
Andrew Wommack:

“He that dwelleth in the secret place of the most High shall abide under the shadow of the Almighty.”

This is a promise of favor and protection to those who dwell in the secret place of the most High (see my note at Psalms 91:14). This is for those who DWELL there, not visit there. This is talking about ABIDING in Christ (John 15:4). This is speaking of those who make the Lord their habitation (Psalms 91:9). *A person can be born again without abiding in Christ.*
Abiding in Christ gives us entrance into the protection of the Almighty. The Hebrew word that was translated “shadow” here is “TSEL,” and it was translated “defense” once in Numbers 14:9 and twice in Ecclesiastes 7:12. Those continuously trusting in the Lord will have Him come to their defense.

God is love (1 John 4:8), so to abide in God means we have to abide in love (1 John 4:16). Those who haven’t heard the good news of God’s unconditional love and grace through Jesus can’t abide in love, and the wrath of the Old Testament Law will keep them from receiving God’s love and blessings.

The Hebrew word “CETHER,” which was translated “secret place” in this verse, was also translated “secret place” in Psalms 18:11. Psalms 27:5 speaks of being hidden in the “secret” (CETHER) of His tabernacle. And Psalms 31:20 says the Lord will hide us in the “secret” (CETHER) of His presence.