(
It was discussed some years ago)
It would be implausible as a generalized feature.
While the division in orders was never set as a cast system where role were totally different (or non succedable), a very important deal for Clergy legitimacy and social place was about being
oratores : the ones that pray.
Even admitting you have a cultural shift radical and world-shattering enough to cause the militarisation of clergy, the direct rivality with
milites and nobility would be enough to force it back off, with huge losses.
Now, as a not generalized, but regular enough in some circumstances? Possibly and not that hard for early middle ages.
After all, Irish monks fought themselves because of loyalties divided along secular nobility, and some bishops or religious if not fighting were present in battlefield (as Odon of Bayeux or Oppa of Sevilla by exemple).
The great change, again, was the appearance of a militaried classes, the milites, concommitent with feudality. Peace of God, and the clear distinction between clergy and nobility, could be turned as "Armies of Peace" (peasant levies led by clergy against nobiliar and milites' abuses) be a more recurrent feature (it would ask for a radically weakened high clergy) but then again, the clear rivality there would be really bad news eventually for a clergy whom main support and familial roots were in the nobility.
No Peace of God movement could as well do it, but will ask for a PoD without strong papacy, and maybe without Peppinid rise (Carolingians clearly set up difference between clergy and military role; and feudalism only reinforced it up to the Peace of God). Huge butterflies would follow.
ITTL, at best, you could have the maintainance of some Bishops, due to their links with nobility, being present on battlefield and fighting on. But it wouldn't be a generalized feature as well.