Replacing early battlecruisers with 9.2-inch cruisers

Would a 9.2-inch armoured cruiser be the ideal replacement for the Invincible class?

For Invincible's original cruiser role, yes; for the later battlecruiser role, Britain would still need Admiral-class-type ships.

The Invincible class's initial cruiser-destroying mission was distinct from the capital-ship role into which battlecruisers later evolved. A new 9.2-inch dreadnought armoured cruiser could replace Invincible in the original reconnaissance and cruiser-combat function. It would not replace the need for fast capital ships once battlecruisers were expected to fight enemy battlecruisers. Admiral-class construction would answer that later role instead.