Any lasting controversy on this topic boils down to a 1940 census document which lists Mary as being both the wife of Frederick Trump as well as a naturalized citizen, despite the fact that she was not granted citizenship until 1942. That
document (behind a paywall), which has an "X" next to her name indicating that she was the one providing the census with her family's information, has the letters "Na" entered in the citizenship status box, indicating "naturalized":
While we can provide no explanation for the discrepancy, there is no evidence to suggest that Mary Anne was in violation of any immigration laws at any time prior to her naturalization in 1942, as she frequently traveled internationally but was able to re-enter the U.S. afterwards.