Well, no. Wilson became President because the GOP split, with the (as Progressive as Wilson) Roosevelt bolting and forming the Progressive (!) Party and the conservatives staying with Taft.
Had the GOP united behind either of them, they would have won easily. Wilson got 42% of the popular vote, while Taft and Teddy between them pulled a little over 50%. More than 6% went to a Socialist Party candidate.
Roosevelt also later sold Korea down the river ~ and boy did we end up paying for that bit of progressive stupidity. That simply encouraged the fascists to take over Japan openly.
Seriously, no Conservative or Republican can look back at Teddy favorably. He betrayed America.