Very little impact. By the time he perished, the die was cast in the Pacific.
Moreover, he was still just one cog in a very rigid command structure
which, though he influenced it by virture of his great popularity, did not
mean he was exempt from that very highly structured geartrain bound by
a vision and system of beliefs clouded by victories long past. IJN remained
a battleship navy in a war that was now dominated by aircraft carriers.
Since Yamamoto never was a friend of power split (you will be defeated in detail), I suppose that Leyte would have been much more difficult for the USN, possibly a completely different scenario.
Not that it would make much of a different outcome, the USN by this stage had a wealth of advantages on their own.
Yamamoto himself answered the question 66 years ago. Asked by prime minister Konoe about Japan's chances in a war against the United States and Great Britain, his answer was "We can run wild for six months or a year, but after that I have utterly no confidence. I hope you will try to avoid war with America".
If I'm not mistaken, the Imperial General Staff (Army) didn't like Yamamoto much, and indeed, were trying to have him killed at one time. He was demoted from "CNO" status to command the fleet, mostly to get him out of town (and where he'd be safer). There were a lot of machinations going on at that time, just before Pearl Harbor.........