Maybe, but there are still a number of problems, even assuming Korolev could have solved the problems in N1's development history that had already been around f

Maybe, but there are still a number of problems, even assuming Korolev could have solved the problems in N1's development history that had already been around for years by the time he died. Let's look at the timeline: Saturn V was rolled out onto the launchpad in May of '66, maiden flight in November '67. In February '66, they tested the Apollo CSM. Meanwhile, N1 made it onto the launchpad in November '67, but wasn't tested until February '69. Even assuming Korolev's survival could have moved up the dates, there's not a lot of time here between test flights to crewed missions. The LOK wasn't even flying until December of 1970, on a Proton rocket since N1 wasn't ready. But even assuming N1 had had its first test flights in '68, how long do you think it would have taken to go from that, to testing LOK, to actually landing someone on the Moon? Probably more than a single year. Finally, let's look at something entirely unrelated to the troubled N1 program: the matter of rendezvous. It was important enough to master that Protect Gemini was devoted entirely to getting rendezvous working as smoothly as possible. The US conducted the first rendezvous in December '65, first docking in March '66, and several more successful tests with Gemini after that (all manned missions), as well as a rendezvous in Earth orbit with Apollo 7 in October '68 and lunar orbit with Apollo 9 and 10 in March/May '69. Meanwhile, the first rendezvous/docking by the Soviets was in October '67, by unmanned crafts that used more fuel than expected, and their follow-up attempt with Soyuz 2/3 in October '68 failed to rendezvous after running out of fuel to maneuver. Their first success with manned rendezvous wasn't until January '69. It wasn't impossible that the Soviets could have gotten extraordinarily lucky on numerous fronts if he hadn't died, but I wouldn't call it realistic, or in fact reasonable.