Why foreknowledge would not make Yamamoto betray Japan

Would Yamamoto warn the United States about Pearl Harbor if he foresaw Japan's firebombing and defeat?

No; he would be more likely to oppose the Japanese Army and try to stop the war from inside Japan than become an American informant.

Foreknowledge of Japan's defeat gives Yamamoto a reason to try to prevent the war in this scenario. It does not establish that he would supply military intelligence to the United States. The proposed alternative is an internal confrontation in which he turns the fleet against the Army. That interpretation separates an attempt to change Japanese policy from serving a foreign power.