A couple of things to consider.
Every Shugenja school I'm looking at here in the books lists Lore: Theology as a school skill.
Second, in Emerald Empire , the glossary entry for Shugenja (pg 272) starts as follows: "A priest of the kami, a religious official in the ranks of the samurai caste..."
We'll have to see if that actually holds up in the lcg and the new rpg. I also remember that some catholic priests or monks (or even priests of other faiths) didn't mind accompanying warriors in history. Of course we're talking about different religions and universes but there's enough leeway there to do many different things. I'd also imagine that shugenja in the lcg will probably remain primarily spell flingers which would only reinforce the notion of a battle wizard and eat away at the whole priest angle.
I don't think the priestly role alone would have any bearing whether Shugenja go into battle in war, get involved in court, go on the road for whatever reason, etc. That would be far more a matter of clan, family, school, and individual -- not something that would blanket-apply to all Shugenja.