No, unification would not be possible without the treaty. You're speaking from a position of ignorance.
Yes, "Republican style of government" is vague and open to interpretation. But it's a logical fallacy to suggest that, because it is vague, it is therefore meaningless. There was a time when those words were the only real barrier between an offer membership to Asylon (and even possibly Aurvandil)– something the mere spirit of unity may have permitted, but the treaty did not.
The treaty, even aside from the guild, has substantively affected realms in ways a mere sense of unity has not. Moreover, there have been numerous times that one nation or another has had an interest in pulling out, and few strong voices were present to prevent that: but the treaty had a role in preventing those actions.
You're right that you can't just write words on a piece of paper and BAM they come true. I'm not arguing that. But the argument that treaties are merely descriptions of power relations, rather than at least somewhat formative of such relations, is wrong as long as at least one party in the treaty conceives of itself as somehow beholden to a law or standard.
And that's the key, really. However vague, the "Republican form of governance" is really a blanket condition covering a set of cultural practices– foremost among them a belief in rule of law. The 'Moot has more in common with the EU or HRE than with most normal treaties. Moot realms have functionally ceded a (rather small) share of their sovereignty to a supra-national entity: the Elders of the Véinsørmoot. They do not do this because of a sense of unity. They do this because the treaty says they should. They agree to the treaty because of a sense of unity, true– but the manner of that sensibility's expression could have extremely wide variation, and can be channeled by treaties, especially and emphatically in a setting where some or all parties operate under the assumption that treaties are a "real law."
Yes, you're right that a treaty can't function if nobody believes in it. Again– duh. That's indisputably true. And you're right that there's a subjective component. But you're dead wrong when you argue that treaties, as distinct from the motivating spirit behind such treaties, are uninfluential.
Indeed, you've all played as rulers: you've all seen the obscene lengths to which most realms will go to argue that they aren't violating a treaty, or are acting honorably, etc, etc. That is compelling proof of my argument. And realms which fail to provide such legal or quasi-legal justification for their actions are usually either hegemonic states who can bully everyone else into submission (rare but does happen), or else become pariah states (Aurvandil).
