No - with just a narrow truck road and no rail system, the Chinese big counteroffensives would have been delayed at least one, and probably two, years.
The postwar effects are interesting though too - without the rails, Burma would have been a much less important oil exporter in the 1940s and 1950s.
And the Burmese state might not have been able to hold together post independence, especially in the north, without the rail and telegraph/telephone networks up there and the additional customs revenue from China trade. I know it is somewhat counter-intuitive because the revolts were many say provoked by a more intrusive ethnic Burmese dominated central government, but tensions always existed with mountain minority peoples, and they might have been able to prevail in breaking away without rail mobility for the central army.
There could be an interesting effect on American domestic politics too. Historians say that until the scandal about the misuse of taxpayer funds in Burma, executive branch pressure on American firms to support the project and similar things leading to investigations and the forced resignations of Henry Morgenthau and Harold Ickes in early 1939, FDR was fully intent was fully intent on running for a third term!
At least before the scandal he was still enormously popular, and I think that could have overcome any public trepidation about overturning the "no third term" tradition. So no President Willkie.
Ironically, the boosted aid program for China from 41-43, of which the Burma Railroad was such a critical part, was one of the things President Willkie was most proud of in his memoirs. If it had not been built though the knock-ons might have meant he never would have been President!