Not well; however:
What if, with whatever POD is needed, MacArthur is Supreme Commander in Europe, while Eisenhower is in charge of the Pacific theater?
Judging by the other threads, there seems to be some consensus that Mac in Europe doesn't end well, but no one really had anything to say about Eisenhower in the Pacific.
DDE actually had a fair amount of Asian experience in his career; he had served in the Philippines in the 1930s, trying to get the Commonwealth Army up and running - so from that perspective, he had some useful background. However, given his infantry and armor background, plus his staff and planning experience, an assignment somewhere in the ETO made much more sense. His record as commander of multiple Allied theaters, and in coalition warfare generally, is without compare; only Marshall and (presumably) John Dill appear to have managed anything equivalent, and Dill was not going to get SHAEF, obviously.
DMA actually had an excellent combat record in France in WW I, so there's that; any criticisms based on assignments in 1917-18 is therefore (presumably) muted; in addition, his previous service as CSA would have prepared him well for the responsibilities of theater command. Having said that, his record at managing coalition warfare in an Allied theater was poor; SW Pacific, as it was structured in 1942, was not a good fit. However, given that the only other senior US officer with the nucleus of a staff available for Australia was Hart, DMA got the assignment. Upon reflection, Hart would probably have been a better choice - he at least had the experience of ABDA behind him, and it is (essentially) a maritime theater. Give Hart an Australian (Blamey, presumably) as a deputy, and ready to move up to theater once Papua and the eastern edge of NE New Guinea has been cleared (Buna-Gona and then Lae-Salamaua, so presumably 1943 or so) and the entire theater would have run more smoothly
and been a better fit for the realities of what Allied forces were available for operations there.
In some ways, the best fit for MacArthur in mid-1942 would have been the CBI; he was imperious enough, and enough of a Republican darling, that he may actually have been able to get the reality of Chiang's China across at the highest levels in Washington, on both sides of the aisle. Plus, I''d expect Mac and Wavell would have gotten along; similar generation.
That also frees up Stilwell, who despite his near unique ability to organize and get the Chinese to fight in an Allied theater, was poorly used in the CBI; given his record in WW I with the French, and his experience with amphibious warfare planning, the ETO/MTO would have been a better use of his abilities.
My .2 cents.
Best,