The best example we have is that of Peter being overcome and called "Satan" by Jesus. But that was before he had been born again of the spirit of God or received the Holy Spirit.
Some will say that Peter had been washed clean by Jesus and therefore had the Holy Spirit...and yet the Holy Spirit had not been sent yet, not until after Jesus ascended to the Father.
But, no, in fact Jesus had even called Peter "Satan" not long after Peter had also been used by God the Father to correctly identify Jesus as the Christ. This is the way of things for those not yet born again of the spirit of God, but not so of those born again. One born again of the spirit of God is not just "touched" or "overcome" by spirits good or evil, but has died. And that new man born of the spirit of God, is One with God, whom is not vulnerable to such evil. None can enter, none can harm such a one. They have passed from death to life.
So, no, one who has the Holy Spirit cannot have a demon. If one has a demon or is being used by and blown to and fro by many spirits, the Holy Spirit is not in him.
But don't take that to mean that anyone who disagrees with another member of the church, does not have the Holy Spirit. Diversities of opinion among the church are another matter: If a finger does not see eye to eye with a knee, it is not because he has a demon. Don't be silly. It is only if either do not see eye to eye with the Head, that would indicate whether or not a demon has entered the body.