Yes, I’d say the Wilson administration was when they first infiltrated the Executive and Judicial branches, via Edward House and Louis Brandeis, respectively. They’d started penetrating the Legislative branch slightly before that—Victor Berger was elected to Congress as a Socialist in 1911, I think he was the earliest one (off the top of my head). By the end of World War I, they already had the start of a lobbying bloc in Congress.
Insidious devils, all.