World-line activation and Okabe conscious state (S;G0)
The life of Rintaro is not a condition to the active status of a world-line. In fact, one example proves it in Steins;Gate 0.
In 2011, >!Mayuri and Suzuha launch their Arc-Light operation. Because they die before leaving with the time machine!<, Okabe tries to send his memory back in the past but the time leap machine>! is not ready yet!< (due to Kurisu’s >!early death!< and the fact that she did not have time to contribute so much to the technology). >!During the attempt, Okabe’s memory fails to reach the target and remains as a backup.!<
In 2025, >!Rintaro is captured and tortured, falling unconscious. Between that time and 2036 he remains unconscious, and the fact that in 2036 memory backup is restored !<proves that the status of a word-line does not depend on Okabe state of consciousness