[Jerry]

Tony,
R1 would have had to reach 2nd Base before the Time of the Pitch to avoid having to tag up; not the time of the hit. (i.e. once F1 begins a motion to pitch . . . I'm paraphrasing . . . is the T.O.P.). What you're describing seems to be a "hit and run" play, where R1 is off and running at the time of the pitch. He'd have to tag up in that case . . . and assuming the situation warranted it. (Not the 3rd out, interference/obstruction, etc.)