Would Archer have founded the Federation of Planets if Daniels hadn't planted the idea of it in his head? Or does the whole Federation exist only because of wibbly wobbly temporal meddling?
I think so, the events of Season 4 would have happened (for the most part) with or without the Temporal Cold War and they seem to be what put the idea in the heads of the various movers and shakers to form an alliance...
While Archer was one of the driving forces behind the creation (invention) of the Federation, it's unlikely he acted completely alone. The Federation as a concept might just as easily have come into being if another Human had been given the captaincy of the NX-01.
Can one person influence history and society that much? Without Archer, the UFP wouldn't have developed? I think that unlikely. The need to unite against the Romulan threat lead to the Coalition of Planets as a defensive alliance. The easing of tensions between the CoP members, especially between the Vulcans and Andorians, would've lead to greater cooperation without Archer's presence. If any one man had a major impact on the creation of the UFP, I'd say it was Admiral Forrest's sacrifice to save Ambassador Soval at the bombing of the United Earth embassy on Vulcan. His act probably did more to unite Humans and Vulcans than Archer. All Capt. Archer ever did was tweak the Vulcans repeatedly (at P'Jem, for example, then when he carried Surak's katra, leading to embarrassing the Vulcan High Command).
True. "Shockwave" shows us there's no Federation (at least not involving Earth) without Archer. In "Azati Prime" and "Zero Hour", Daniels gets very angsty at the prospect of Archer dying before he can fulfill his destiny.
Perhaps Archer's actions as President of the UFP involved preserving the alliance in its early years. His actions as a Starfleet officer were probably less important than his political decisions and influence as an ambassador to Andoria and UFP council member.
His connections with certain important people on Vulcan, Andor and possibly elsewhere may have been especially crucial in the early days. Sometimes, it really is all about WHO you know.
In "Shadows of P'Jem", Humans, Andorians and Vulcans are working toward similar goals over Coridan. Brokering peace would've occured to somebody eventually, and that was before Daniels began dropping hints to Archer in "Shockwave, Part II". Although the continual quid-quo-pro between Archer and Shran, and him having something to prove to Soval might've been the most instrumental part. It's a little acorn growing into a tree from there. You could write the Temporal Cold War completely out of existence. So long as Archer doesn't get along with Vulcans, he gets out there and encounters Andorians under similar conditions, having that one thing in common.
Naturally Archer had a huge hand it in but he wasn't the sole reason it started and it would have happened sooner or later without him. He definitely helped bring the Andorians into it. Though it was nice to see him at the start of the Federation.
But remember, it was Archer who convinced Shran to sit down and negotiate with the Vulcans, because Archer was the only human Shran trusted. Without Archer, Andor and Vulcan would have most likely remained at war. Same goes for Tellar vs. Andor - when the Tellarite ambassador gets into it with Shran, it's Archer who helps defuse things.
Well, that means Archer was instrumental in building a relationship between Humans and Andorians, and between Humans and Tellarites, but not between Humans and Vulcans. Humans and Vulcans were pretty close without Archer's help. I will think he did more to jeopardize Human-Vulcans relations; things remained cordial between Earth and Vulcan despite Archer, not because of him.
Which might have helped the formation of the future Federation. If Earth and Vulcan were too close, then Andor and Tellar could have felt like junior partners, instead of all four coming in initially as equal partners.