Indeed. One might as well ask "WI Obama had chosen Charlie Rangel as his running mate in 2008?"
Or Kennedy had chosen John Pastore in 1960 - why not
two northeastern Catholic liberals?
Prior to 1948, Presidential candidates did not just choose their running mates. Even FDR had to fight to get Truman in 1944 and Wallace in 1940.
So one might ask "WI the Democrats in 1912 had chosen Tom Watson of Georgia as Wilson's running mate?" (Watson was a hard-core race-baiter and Jew-baiter. The Ku Klux Klan would have been even more delighted than they were with just Wilson. Watson was also a former noted Populist who would have reinforced Wilson's "progressive" appeal.)
Or "WI the Republicans in 1860 had chosen Cassius Clay of Kentucky as Lincoln's running mate?" (Clay was a fiery Abolitionist, and in fact Clay was a respectable second on the first VP ballot.)