It is not entirely clear that one should even classify the Pacific Theater in this way. For one thing, there was much more than just aerial bombing involved. Consider the naval battles, the island hopping and invasion, the mining of ports, the fighting in China, etc. Separately, it is still historically disputed whether the strategic bombing, in particular the atomic bombing, actually was what caused the Japanese high command to surrender when it did. The other leading candidate reason is the declaration of war against the Japanese by the Soviet Union, and their steamrolling of Japanese troops in Manchuria. The idea of a combined US-Soviet invasion is much more a "boots on the ground" sort of threat than just an aerial bombing threat. Such is the argument. The strongest presentation of it is Hasegawa's Racing the Enemy, if one is interested in following it up.

I have heard it said that if the atomic bombs were credited with ending World War II, then it would be the only time in history that a war ended because of aerial bombing. This is deployed as an argument by those who argue that the atomic bombs probably didn't end the war — that they would be historically anomalous. I don't necessarily buy that as a strong argument (I mean, maybe the atomic bomb was anomalous — there is no logical reason to supposed it was not), but it implies the answer to your question is "no." I suspect part of this is going to come down to what you define as "won" and what you define as "only with an air campaign."