No, the original Classic server(s) did not have storylines. All versions have maybe had a few explainations for things at the start, a few bookshelves with pieces of random information, a few signs, but that was it. The 'story' was never focused on and certainly didn't apply to any quests after the initial few; those seemed to make it up as they went along. Thor's Classic is really the only attempt at a storyline-led server.

I am not against the idea, but most of what is being referred to in this thread is not true.