In answer to that question; no. A lot of players finish the game before oil is revealed on the map. I'd think that if you didn't have yourself in a dominant position by the time oil is around, say, dominant enough to be guaranteed oil, or guaranteed victory over someone that has oil, then you are pretty screwed as it is, oil or not.
Not true, necessarily. You could be well on your way to a culture victory, for example, having turned off research after Liberalism/Nationalism.
Or you could have beelined Mass Media, built the UN and remained the tiny little civ that was everyone's buddy.
Heck, even a good peaceful space race gets no benefit from oil.
The main thing oil is important for is if you want military (conquest/domination) victories. Then its pretty necessary if (and only if) you are playing a game that drags all the way to the modern era.