Mark Hanna, as you know, was a close friend of William McKinley and the chief strategist (as well as a financier) behind many of his political ventures. Hanna apparently loved to play kingmaker - before he backed McKinley in 1896 he, together with McKinley, backed John Sherman of Ohio for the GOP nomination in 1888.
In his later life, Hanna was greatly opposed to Theodore Roosevelt. In fact, Hanna had been considering a run for the White House in 1904 to challenge Roosevelt; he died before anything could transpire.
I ask you not just whether he would have run for president had he lived, but whether he genuinely desired the office or desired simply to place people (Sherman, McKinley) in it or bar people he objected to (Foraker, Roosevelt) from it.