I guess "fall for" may be too strong. However, his strong desire to race off and bag Japanese carriers and failure to make sure San Bernadino was covered by somebody essentially allowed Ozawa's decoy force to be just as effective as if he hadn't known what its mission was. The Japanese plan was working by dumb luck and only Kurita's timidness off Samar in the face of American courage averted a worse disaster for the US.
One thing to remember about Kurita's force is that it turned around for several hours after withstanding numerous attacks from Halsey's carrier aircraft. Halsey thought that he didn't need to worry about Kurita and Nishimura any more because they were out of the battle. That is why he went after Ozawa when his scouts spotted the carrier force. He didn't realize that Kurita had turned back again and was closing in on the beaches and transports. That said, Halsey still should have stayed closer to the landing fleet and let the typically complex Japanese plan play itself out, then pound them in detail. He especially didn't need the battleships against a force that lacked similar firepower.