If Ireland was able to exert full control over its Church, it could have provided an example for other nations in Europe as well. A Catholic Anglican Church in England, a Catholic Iberian Church in Spain and Portugal and so on.
Depending on what you mean by that, 'Ireland' didn't 'control' its church. There wasn't any Ireland, in the sense of a single government or anything. In terms of culture and language, then sure.
If what you mean is that the church controlled itself, and was independent from Rome, that could certainly lead to less Papal control over e.g. France and Spain. OTOH, it might lead to MORE control, as they differentiate themselves from the 'heretics'.
The OTL churches of England, France and Spain that pursued their own goals and fought control of the Papacy (breaking off for the first, and controlling their own national churches within Catholicism), were politically inspired to do so, it was Kings' policies not evolution of local denominations that mattered.
Could we have seen a bunch of autocephalous, autonomous churches like the Eastern Orthodox churches. Yup, we sure could. Could we some unitary, but very decentralized church? Yup. In fact that's what the 'celtic' church was OTL.