Babe Ruth still has one of the fastest documented reaction times ever measured. The science was new at the time, but the data was repeated and compared against modern athletes over the last 100+ years. It is possible that pitcher could strike out Babe (BR also struck out more than nearly every player), but I sincerely doubt he could consistently strike out The Bambino in his prime.
A better question for this pitcher is how he would hold up if he pitched 35 complete games (Babe pitched in 41 games that season), as Babe did for the Red Sox in 1917? Would he win 24 games in that kind of a season? Could he hold up if he pitched 330+ innings per year? Could he pitch back-to-back days?
And finally, does he think he could break Babe’s AL record of shutouts in the postseason (a record Babe still holds)?