Christ's presence is all of Him, all the time.  It is only our ability to perceive His presence that is the problem.  We are all, including Christ, matter and spirit, intermingled and intermixed.  It is a convenience to try to make a distinction between matter and spirit, but it is a limit of our human ability to perceive beyond the physical.  God is bigger than that.

I believe that it is the community praying together, recognizing their bond and love together with Christ, that makes it possible for some to better realize His presence.  It isn't some magic of the priest that makes Christ present, but the joining of those who love Christ that makes the difference.  Christ's  presence is also realized in quiet, private, contemplative prayer.

The Eucharist is not a magic show, as someone I recently read so aptly put it.  Christ is present were two or more are gathered in His name, no priest required, although I like ritual and group rituals require a leader.