most likely not! though it is not confirmed but i do think regardless of what age haru is, if he did not encounter any kitsune; or tamamo herself, the divine powers wouldn’t awaken.
since kitsunes are highly related to divinity! this way it makes sense (=・ω・=)
i think that, for seimei’s case, he was connected with not one but multiple kitsune therefore his abilities were far more advanced!

Woaahh Haruaki's slowly awakening Seimei's powers after his prayer beads broke.
Seimei awakened his powers of divine sight and mind reading at a mere age of 5, I wonder if Haruaki would've awakened it too at that age if his powers wasn't sealed by the prayer beads when he was younger??