Marshall, like most members of the US military before WWII, was fairly non-partisan. He thought that military officers shouldn't belong to political parties because the military should be seen to be above partisanship. Eisenhower was in many ways similar. As late as 1952, Democrats felt they could draft him as their nominee. Like Eisenhower, if Marshall was in a position where he was being drafted, he'd pick a party somehow.
Marshall was associated with the Democrats because of his involvement with Truman, but that was done out of a sense of public service. I don't know if he would have self-identified as a Democrat. Someone who knows his biography better might be able to confirm any partisan leanings.
Marshall was originally intended to lead Overlord. FDR eventually overruled that because he felt Marshall was too valuable to the war effort in Washington. If that changes for any reason, Marshall would lead Overlord and essentially take over Ike's role in history. Ike would probably either be an Army Group commander like Bradley, or perhaps remain in Italy.
PODs could be either that FDR decides to send Marshall to Britain anyway and pick another person as replacement Chief of Staff, or that Marshall was never selected as Chief of Staff in the first place (originally many people thought Hugh Drum was going to become Chief of Staff instead in 1939) leaving him available to be selected for Overlord.