I can't see why not - an Australia freed of British foreign policy would have to make its own decisions and choices, and an alliance with Japan would make sense, and wouldn't require changing immigration policy. Japan would be making its own decisions based on its own strategic interests, and not do more than symbolically request any changes - after all, the US policies didn't create a rift in this time period.
Obviously, the exact course of events is important, but in a CP victory timeline its possible that Britain has agreed to hand back German colonies occupied by Australians, and Australia may be looking to refuse but need a strong ally so that Germany doesn't try it by force
Alternatively, Germany may cede most of its Pacific possessions and then Japan and Australia could end up near neighbours
Best Regards
Grey Wolf