no empire lasts a thousand years.
The series Enterprise seems to say that Earth was the driving force that brought the original members of the Federation together. Without Earth, the other founders would have just gone their own way.
Debatable, the Romulan War wouldn't have happen, the Romulans wouldn't have later been penned up behind the NZ in the 23rd and 24th centuries.
But would an Axis victory have prevented the Earth from becoming involved in Intergalactic society? Would the people of Earth never have overthrown the tyranny of the Axis powers? Would defeat in WWII for the Allies have meant that Earth will be dominated by the Axis powers for centuries to come or is there something else that Axis victory would have done to prevent Earth from joining the Federation?