A lot depends on the 'Class A' amplifier. Do you mean class A transistor- maybe, if class A transistor amps do not improve at all in the future- which is unlikely.
Given that class A tube amps will not improve at all in the future :), again maybe.
Overall you will see Class D take over the bottom end of the solid-state market, and make forays into the high end. Since it is not a mature technology yet, price/performance curves *do* suggest that class D will be challenging the current art. But not today. Give it 5 years and lets see if conventional technology does not improve as well.