I have never heard nor read anything that would indicate such a ‘priest brigade’ ever existed, at least not on any large scale that would be considered as a military unit. I see them as being very much in line with the Druids from RTW (which was also a unit that CA showed off before launch.) In both cases, I see the unit as representing not so much actual players on the battle field, but a representation of the influence that both groups wielded both on the common people and on the leaders, in terms of morale and whether or not a particular choice was just and/or wise.
As to their reality/fantasy, I think that would be very hard to show either way with ‘hard facts.’ At best one must make some conjectures as to their place. I have no doubt that throughout modern Christianity that priest have participated in battle. It is also possible that priest participated during the time that BI occurred. The specific prohibition against a priest shedding blood or taking a life did not become official scripture (Cor 11:26) until the end of the BI time frame, a time period where many ‘versions’ of Christianity were in existence and a struggle was going on as to dominance. As such, versions of Christianity that did not prohibit priest participation in shedding blood and killing might have existed.
By the middle ages, while the church had many military orders, the ranks of these orders were not filled with actual priests, but with feverent faithful (well, usually….hopefully….ok, sometimes.) The bottom line, this was most likely due to the fact that there weren’t that many priests. Add on to that the fact of the immense cost and time required to train someone for the priesthood (indoctrination, reading and writing, history as far as the faith is concerned) and the few priests that did exists certainly would not be wasted in something so risky as a battle. So while a few priests here and there might take up the club (or sickle) it is unlikely in my opinion that they did so in any organized military size groups.
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