Marshall would be more willing to compromise on reservations to the Vesailles Treaty than Wilson was, and because of this greater flexibility--and because of Wilson's "martyrdom" on behalf of the League and because most Americans wanted a League of some kind--he would probably be able to get the Treaty and League through the Senate. (The so-called Irreconcilables, who objected to the League in any form, were a small minority in the Senate. One can argue that some of the so-called Strong Reservationists like Lodge were really Irreconcilables in disguise, determined to find some excuse to defeat the treaty, and that if Wilson would have agreed to the Lodge Reservations, they would have demanded further ones. But I doubt that they would have the votes to do so successfully even with Wilson, and in any event, such games would probably be politically impossible after Wilson's death.)
The Republicans will win in 1920 in any event--martyrdom or no martyrdom, too many people ranging from German Americans to African Americans would be just fed up with the Democratic administration.
I doubt that US membership in the League would make that much difference, but there is one interesting way Marshall's administration *might* have differed from Wilson's, if Marshall had come to power early enough: in April 1919, the New York Times quoted him as saying that he would favor sending "a sufficiently large force to Russia to thoroughly exterminate the Bolsheviki."
https://books.google.com/books?id=po0bAAAAMAAJ&pg=PA14 Whether it would really have been politically possible for him to do so even at that time is another matter; and by October 1919 it would almost certainly be too late.