Would more carriers accelerate anti-aircraft armament?

Would widespread light-carrier construction make navies take anti-aircraft weaponry more seriously?

Yes, though Germany in particular would remain constrained by the loss of research and industrial capacity after the First World War.

More navies operating carrier aircraft gives every fleet a stronger reason to invest in anti-aircraft guns. Threat recognition does not erase industrial constraints: the Treaty of Versailles and the postwar dismantling of German research and construction capacity still determine what Germany can actually build.