Interesting idea, but I'm not so sure it was an R1a vs. R1b battle. Let's look into the major players and their major haplogroups:
Allies:
USA: R1b, I1
UK: R1b, I1
France: R1b
USSR: R1a, N (though Stalin himself was a G)
Axis:
Germany: R1b, R1a (both), I1, I2
Italy: R1b, J
Japan: O