Yeah, most likely. A lot of it'd probably be policy he'd have approved of anyway, both IRL and ITTL - IRL, we all know what he was like, and ITTL he seems to have kept OTL's dislike of unregulated business and wants to ensure the citizenry are cared for, he just disagrees with the Radical Socialists. Plus, the US was taking a lot of cues from Germany, and the Kaiserreich had a lot of similar legislation (Bismarck's efforts to cut Socialism off at the knees by meeting workers' needs). Add to that a more powerful central government in the TL-191 US anyway, and I can see a modus vivendi like this being reached.
Agreed. All of which are aims that I'd agree with...
This could actually be seriously good TL...
EDIT: Here, this could also be good for the TL-191 Socialist Party. A Grand Compromise with TR could sideline any of the more Radical elements, empower the more moderate parts. Which would work out to their advantage in future elections and in shaping policy.