No.
In the traditional problem, the man tied to the tracks has no input in the final result, they are just a passive piece of the problem, we can assume what their thinking is and that it is how I rationalized my solution: I would expect the lever to be pulled if I was tied to the tracks and so I pull it myself knowing I would not blame the one pulling the lever for my death.
But in this scenario the man has the ability to act for himself: he can decide to jump. I would never expect him to do so (actually I would never expect 99% of people to pull the lever if they were to die themselves) because that is an action that goes too much against all of our instincts and by pushing them I would, in my opinion, commit a murder.
If I was the fat man I would not jump, and if I was pushed I would absolutely blame the one doing it for my death.
You could think that killing 1 to save 5 is the better outcome, but who decide that 1 human is less worth than those 5? It’s just the numbers? Then you could argue that between fighting WWII and submitting to the Nazi the better outcome would have been to not fight them because the people that died in camps were less then the victims of the war. Of course that’s an overblown example, but it show why I’m extremely uncomfortable with pushing the fat man: imposing your will on someone who has the ability to act is almost never the answer
According ti a quick internet search: https://www.freefixer.com/library/file/oalinst.exe-66409/