I suppose a fringe pattern would develop regardless of September's mistakes and Peter's existence or nonexistence.

The original intended timeline would still allow for the technological advances necessary for infiltrators like Newton and other shapeshifters to cross universes.

And William Bell would still prepare for an upcoming war by authoring the ZFT manifesto and conducting the Cortexiphan trials.

And in any timeline Bell would anticipate inevitable conflict between Blue and Red universes by insisting: "a storm is coming. Perhaps the last and worst storm of all. And when it is over I feel there will be little left of our world."

Also, I ran across this intriguing theory posted on fringe-forum by a user named hanchueh:

The two universes were always destined to be linked and cannot exist without the other.

Without the proper "bridge," the two universes will destroy each other one way or the other. Even if Walternate finds the cure, and Red Peter grows up in Red universe, someone, either under Walternate's DoD or a rogue group like David Robert Jones, will eventually cross the universes and start the deterioration/destruction. The only way to stop the destruction is to have a proper link where forces cancel out each other (the Eye of the Storm a few episodes ago, anyone?).

The key to stop the destruction is Peter Bishop, who is the only person that can stop DRJ, one way or the other. Blue Olivia is also important because of her qualities and interactions that influenced Peter into a good person and a hero. Peter was going to grow up with a broken family (Walternate had a mistress and Blue Elizabeth died young and Walter wasn't a good father either) and was going to become a bad person as a con artist until he meets Olivia, who with dedication, ethics, and responsibility became Peter's first true friend. The future Walter knows this, so he built the machine with Peter as the operator and Olivia as the fail-safe. It's the only combination that would ensure the survival of the universes.

In any timeline, the machine would always be built either as a weapon to destroy universes or as a bridge to permanently link them. Peter and Henry are important not because they are the ancestors of the Observers, but because they (and their descendants) are the only people that can use the machine. Only the RedPeter/BlueOlivia Henry would grow up to become a good person not to abuse the machine because only this Henry has a complete family all with good qualities, especially with a kind Walter who knows the consequences of misused science as a grandfather. A Red/Red Henry would be in control of Walternate who is too ambitious and too close to the military to become a weapon one day. It is also worth mentioning that Walter saw his own ambitions as a major flaw early and had William Bell remove parts of his brain that would allow him to become Walternate. Either that or William Bell saw the flaw and decided to remove the parts on his own.

The Observers' purpose is not to ensure the existence of someone who would become their ancestors. They exist outside of time and can always visit futures where Observers don't exist. Their only purpose was to observe but later becomes to stop the inter-destruction of Red and Blue universes (perhaps because this destruction starts a chain reaction to destroy all other universes). They realized that Peter is important because of the machine and because of him being "Bane of DRJ," but with him and his descendants being a problem such that they can always become "Destroyer of the Universes" by misuse of the machine, the Observers decide to try the one possible solution of erasing Peter after the universes are linked into the Amber Universe.

A new problem comes in the form of palimpsest: the overwritten Amber Universe has pieces of the original Blue and Red that can bleed through. The Observers think they can just overwrite the bleedings over and over. September alone realized this is not the best solution and decided to put the fate of mankind back in mankind's hands: let Red Peter and Blue Olivia reunite and believe in their characters that they together will make future better and ensure their descendants to never be corrupted into weapons.

Peter must go home, and Blue Olivia is his home. They complement each other. They support each other. Together they can overcome any problem even villains like DRJ and Newton.