A question occurred to me, with a stabilized Brythain and Church, would the "celtic church" (ie: hiberno-scotish missions) still form? If so, would it be prominent enough for the Archbishop to call a synod to bring it inline with Brythain?
More likely if a Brythonik Church is formed Hibernia and Scotland will be brought under it, especially due to the fact that a Archbishop in Gloucester is essentially a permanent Papal nuncio.
If the Hiberno-Scottish Missions are brought under an Autonomous Brythonik Church, the "Celtic" Church would be basically fully recognised. The reason for this being that the "Celtic" Church was basically a set of "deviant" practices that fell outside of the usual Roman church life, some of these like Irish Penance were eventually adopted by the Roman Church in the 1200s. Under an Autonomous Church such practices would have been recognised as a part of the Liturgy and allowed. This is also coupled with the fact that generally even at this time the Irish were quite pious, and so likely would have produced more priests, especially if Brythain has a focus of war.
Similarly, in my view the difference of the "Celtic" Church is overstated, at the time most differences were in calculation of easter, which would likely be brought in line with Rome, the Method of private confession rather than public trial, as was traditional, a different tonsure, and a form of harsh pilgrimage, where you left your home area forever, voluntarily. Of these the Confession, Tonsure, and Pilgrimage would likely survive, and the easter would likely be changed to be mainline. Some have accused Insular/Celtic Christianity of being Judiazing which appears to be true in places, but I dont think it can be taken to be fully seriously, due to the pain involved in cutting the foreskin.
So more likely the "Celtic" Church would be formalised by this rather than crushed.