Does GTA V's main campaign have full coop play?

I haven't played GTA V yet, but there were a lot of rumors that the main campaign would possibly have full coop play. But when I search for GTA V and Coop campaign, I mostly get articles on how it's probably coming or GTA online.

Does GTA V allow the main campaign to be played coop?

The main campaign is single player only but there is to be co-op play online. Multiplayer is meant to be a persistent world where players do take on co-op missions (as well as the usual array of MP game modes).

Watch the multiplayer teaser video to see what's included online...

No.

I was just able to find the answer at GTA V: Burning Questions Answered:

Why a single-player story with multiple characters? Why no multiplayer co-op?

It would be impossible to do that and keep the level of precision we've got in this. You could make a great co-op game, but we felt that we're doing other bits of our multiplayer that will fulfill those desires in ways we think are very fun.

Strictly speaking you cannot experience story mode via multilayer coop over the network as everyone already mentioned. However there is a mod, which allows to mimic this.

Multiplayer Co-oP Mod allows one to share the same world with anyone connected to the same server. It also allows one to share one's NPCs and traffic. You cannot harm other's NPC though. That said closest one can get to experience story mode on coop is by starting the story mode at the same quest and connect via aforementioned mod's server to share the world, but not sharing NPC in order to avoid doubled NPCs on screen. This will mimic coop play as best as possible. This method has limitations along with mentioned inability to kill other's NPCs and some glitches, but this allows for a feeling like playing in the same world. Also there is a possibility to enter as passenger to other's cars by pressing G.