No, it doesn't. That's not what Patriarchy means. Patriarchy doesn't actually give dominion to all men over women. It gives dominion of women and most men to a few men who hold all the resources.

But that doesn't mean those men can't be manipulated because men are vulnerable just as much as anyone else. Look at the Biblical Patriarchs. Every single one of them had "God's will and plan" for them brought to fruition by behind the scenes manipulations of their wives.

Not having structural power doesn't leave you with zero agency. It's just severely stunted. You're limited and always vulnerable.

Holding structural power doesn't make you invulnerable. There will always be those looking to take you down or undermine you.