Do I need to play past a certain point to play online?

Solution 1:

I can confirm that you are indeed required to complete the prologue of the game before you can play online on PC. I tried to jump straight into online and was in turn, forced to complete the prologue. (a relatively painless experience)

In theory it shouldn't directly disrupt the missions or story, but you do deal with story characters to collect some of the more fun online missions and these tend to coincide with their single player counterparts.

You could always just do the unrelated missions such as Team Deathmatch or Races.

Solution 2:

You can automatically play online. While it is recommended that you at LEAST play the prologue/tutorial you have the freedom to immediately jump into Multiplayer.