Can you be "included," in Christ, yet not "have the Spirit"?
The reality presented in Scripture (and I am indebted here to helpful comments from Dr. Joseph Tkach and Dr. Gary Deddo), is that the Spirit is always working with everyone (believers and non-believers alike). However, it is believers who are both aware of and receptive to the Spirit's work. While all people have been reconciled to the Father through Jesus' vicarious humanity, not all believe - and thus not all actively participate in God's new creation of humanity in Jesus.
Thus there is a difference between believers (those who embrace their inclusion in Jesus) and those who have yet to do embrace what they have already been given. So when Paul says, “If anyone does not have the Spirit of Christ, he does not belong to Christ,” we understand him to mean that though all are included (loved, forgiven and accepted by the Father), not all believe this, and thus not all actively participate in the life that is theirs with God, in Christ.
Paul tells us in Rom. 5:10 that we were reconciled to God "when we were God's enemies" - not when we "turned to God" in belief. Reconciliation on God's part toward us occurred prior to any personal response. In Adam, all humans were God’s enemies, but now through Jesus' life, death, resurrection, ascension and his pouring out of the Spirit on all flesh, all humans are included in Jesus (the last Adam) and are thus no longer God’s enemies; no longer condemned; but reconciled; forgiven; accepted; and unconditionally loved as God's dear children. That is the gospel (the good news).
In Rom. 9, Paul exhorts believers (those who embrace God's reconciling work, in Jesus, on their behalf) to actively, through the Spirit, participate in their reconciliation (inclusion) in Christ. This is what Paul means when he writes of "walking in the Spirit." All are included, but not all walk in the Spirit. In that sense, not all “have” the Spirit - it is not the defining, dominant reality of their lives. Indeed, to "belong to Christ" is to believe, receive, and through the Spirit, actively participate in Christ's continuing human life.
But note: we can't share what we don’t already have. Our belief (faith and repentance) does not create our reconciliation (our inclusion; also referred to by Paul as our "adoption") - it does not create our true identity as God’s children. Rather, we believe because we are already included/adopted. Through belief, we come alive to what is already true. Like the prodigal son, we turn our hearts to the home we already have with the father who already loves and accepts us.
Note also that no one is able to declare that Jesus is Lord, except by the Spirit that draws them to the Son. Thus personal belief is, itself, a sign of the Spirit's presence with, and work in, that person prior to their belief. Then as a believer responds to the Spirit's work, there are deeper "fillings" of the Spirit in their life of growth in Christ. This filling is not some sort of mechanical, automatic, cause-and-effect process - indeed it is part of a dynamic, ongoing relationship with God, made possible for us by Jesus as, in the Spirit, he shares with us his transformed humanity. Jesus opened the door for all of us to be indwelt by his very Spirit.