Hmm.. so is it generally the the opinion that a Theodore Roosevelt presidency in 1912 is either virtually impossible (Taft car accident?), or unlikely to significantly increase the the likelihood of a US entry I to the war (at least if Britain is neutral)?
What TR, Root and other war hawks feared was precisely that the war might lead to the destruction of the British Empire, leaving the US alone to face Germany. (Even so, they were clearly a minority in the country and did not even dare to call explicitly for the US to join the war until 1917.) A purely Continental war would be something different. The US would be about as likely to enter it as it would have been to join the Franco-Prussian War.