I thought the same thing but i wasn't sure so i thought asking was better.

Thank you for the answer. I was wondering because it only said: "Beat the Ceadeus from a new game.", "Time starts on first input from talking to the village chief." and "Time ends when the "Quest Complete!" textbox appears after repelling/defeating the Ceadeus." and never said something about Offline/Online. It seemed a little bit suspicious to me so I wanted to ask that first before wasting 4h for nothing.

Btw: Tanzia port is offline and online. ;)

I was just interested if it would be ok for this runs to go online and get pulled through low and highrank quests for farming equipment because there is nothing in the rules that this is forbidden.