Too what degree will we be able to effect eccliesiastical policy in our realms? I ask because it greatly impacted politics in this time period. For example, Ireland finally adopted a dioscesan (sp?) system during the CK time period (before the Norman invasion) over its older monestary-based one. This was due in part to pressure from various Irish kings. In CK terms, one could say these Kings wanted to increase their Peity ranking so they would be seen as more legitimate in Europe. So even without having control over any bishops, a dynasty should be able to influence church policy.
On the other hand, they shouldn't be able to influence too much, because the church could and would dig in its heels if it thought its independance would be threatened (i.e. Becket)
On the other hand, they shouldn't be able to influence too much, because the church could and would dig in its heels if it thought its independance would be threatened (i.e. Becket)