Yes, you *could* do that. But having an actual religion behind you makes it a lot more convincing.
A lot more distracting. And expensive. If you want to blast these heathens, then you'd be much better off spending these thousands of gold you'd spend on local temples into troops instead, and these nobles you'd have as priests leading troops instead.
I wouldn't go so far. However, I agree with your basic point: the interest of the religious game is in influencing other nobles. All the game-mechanics options for priests are technically influencing peasants; however do not think you can get away with any of them without at least some powerful nobles backing you out.
The point of a religion is to create a culture among a noble group. Once that culture is in place, the Lords will build temples for vanity. I doubt doing it the other way around can be fun.
You can't get away with them without noble support, but you also can't use them at all without follower %.
You can also create a religious culture among a noble group without needing for one lord to spend hundreds of gold to be turned into a
pop star priest. What's fun about religion is creating that culture and sharing it with others, not clicking on preach for a few days in a row, then travelling next door to start again.