No, nothing like that. A couple of things...
I don't believe you can belong to God and not be indwelt by the Holy Spirit, regardless of whether you are an OT or NT saint. I believe Romans 8:9 is a universal truth just more fully explained and experienced in the NT.
When I say a different manifestation, I mean the Holy Spirit has many different functions. One of His responsibilities is to convict the world of sin. This would include believers. So when we fall into sin, He will come to the believer and bring this to their attention. If this is resisted, He will bring chastisement. His purpose is to bring us to repentance and back into fellowship with the Father. He also guides our steps as we walk by faith, leads us in truth, and a host of other things.
I do not believe that once the Holy Spirit is given that He ever leaves us. I believe God loves with an everlasting love and once He sets His affections on an individual, He will love them throughout eternity.