Could the big cats have introduced British triple turrets earlier?

Could triple turrets on the big-cat battlecruisers have changed later British battleship development?

Yes. Building an earlier battlecruiser with triple mountings could bring the technology into construction sooner and change the choices available to later designs.

The alternative development path places triple turrets in an earlier battlecruiser programme. Such arrangements had been considered as a way to increase firepower while reducing the proportion of weight devoted to the battery. Building one of the big cats that way would put triple mountings into construction before later battleship decisions. The consequences remain counterfactual, but earlier manufacture could change the options available for Queen Elizabeth and her successors.