I have been speaking to a Roman Catholic friend, and his argument for the validity of the papacy was that John was still alive for the first pope, and there was no record of him speaking against it. Is that true according to your knowledge?

This is an argument from silence! John never spoke against nuclear energy, or abortion, for that matter. In logic, this is not a valid argument. 

Moreover: There was no pope at this early point in time. The first real pope was centuries later! Secondly, take a look at the verse in Revelation where John falls down before the angel. (Similarly, when Cornelius falls down before Peter in Acts 10, Peter rejects this abject obeisance.)  Now if John was rebuked for falling down before an angel (!), why would he support human beings falling down before a mere man?