The plan was to invade Kyushu, yes, starting in November 1945. Depending on how that went, there were plans (not approved yet by Truman) to invade Honshu.

And the Soviet Union was going to cut off Japan's supply lines in Manchuria and Korea. And the US had already begun mining Japanese harbors to prevent further resupply, and had bombed out (conventionally) nearly every major Japanese city (and many minor ones).

All of which was the plan even with the atomic bombs — the atomic bombs were in no way imagined to be likely to end the war by themselves, and the plan was always to bomb and invade.

Whether Japan would have "fought to the last man" or whether it would have folded fairly soon anyway (the Soviet declaration of war shook even its hardliners to their core, and the Japanese military had predicted that they could not survive a dual invasion) gets into the realm of speculation. There were those in the Japanese high command who wanted to end the war well before that; and there were militarists who were banking on a "bleed out" strategy. Which of these would have prevailed in such a circumstance is not possible to know. Certainly the US was surprised that the atomic bomb and the Soviet invasion (both nearly the same time) seemed to have gotten the Japanese high command to capitulate; they were not expecting the end of the war to be as fast as occurred.