Why larger treaty allowances may preserve the naval balance

Would larger ships gain the same advantage if every navy had comparable tonnage allowances?

Broadly yes. Rival hulls and weapons would also grow, leaving similar relative problems at a larger scale.

A larger tonnage allowance would apply to rival navies as well as Britain. Bigger ships could become more survivable, but the weapons intended to fight them would also develop against that higher standard. The result could preserve much of the historical balance between designs. Britain would gain a different advantage only if it received an exceptional allowance denied to its rivals. Larger ships would also require more investment in infrastructure.