When you're in the Holocabana for Stellar's funeral the chaplain is described as a "holo-chaplain", which means he must be a hologram. However, he leaves through the Pneumatic Tube. If he was a hologram, he wouldn't be able to leave the confines of the room. Also, looking at the chaplain outputs: "Stunningly real, don't you think?".
It is possible he had a mobile emitter like the holographic doctor in Star Trek Voyager