[Fantomen]

No, patrolling does not affect dominion at all. Patrolling decreases unrest (while killing some population in the process) and has a chance to find hidden units.

So patrolling is useful to get rid of general unrest (from events or spies etc), to find hidden enemies and to keep unrest down while bloodhunting or overtaxing.

To counter any form of attack on your dominion (Blood sac or other dompush strat, hidden enemy priests or prophet, heretics and melancholia) you have to build temples, preach and/or get rid of the source of the problem, by killing the enemy unit/nation in question or herd your heretic units into a dedicated province.