The process of the war itself had a hardening effect on the 1861 Confederate state: for most of the war there was no single military hierarchy but by the last year this was junked and Lee was officially made the General in Chief of all Confederate Armies. I don’t know what the timeline is here for Confederate victory, but the process of learning through war I think would ensure some degree of post-secession centralization in order to survive.
There is your catch 22. The Confederacy of 1864 was fairly centralized. The Confederacy of 1864 was broken and on its last legs, near bankrupt with its manpower depleted. That's not a good negotiating position to ask for Arizona, and a worse position to conquer it from.
On the other hand, the Confederacy of 1861 may have had the collective resources and willpower to go after Arizona, or in the case of a victory, to claim it at the negotiating table. But this was also the most decentralized and incapable of adventurism.
I completely agree that a successful Confederacy would want to be expansionist, they made no bones about it. There was that whole Knights of a Golden Circle, with designs all over the Caribbean and Central America and even into Colombia and Venezuela. But wanting something is not the same as being able to take it. Historically, the only successful Filibuster was Texas. Other attempts to hive off Mexican promises failed disastrously. The Celebrated William Walker lasted barely three years and only managed to unite all the rest of Central America against him. There was a certain racism at work premised on the notion that a handful of white adventurers could take a country away from the native residents. In Latin America, that didn't always work out.
Expanding into Mexico is probably a non-starter. Expanding into the Caribbean brings the Confederacy up against the British Empire, and the French Empire, and the Spanish Empire, and the Dutch Empire for that matter. Two of those would swat the Confederacy without breaking a sweat. The third, the Spanish, remained a formidable naval power weill into the 1880s, and the liberation movements in Cuba were all abolitionist - it's hard to see the Confederacy succeeding against Spain either on the sea or in Cuba.
And of course the US would likely invest a lot of time, treasure and energy in frustrating Confederate ambitions.
It's hard to imagine the Confederacy successfully conquering or negotiating for Arizona. As you've said, a lot depends on when and how. But there's a paradox, the more able they are to take it, the less likely they'll have the will to do anything with it, the more organized and centralized they are in order to develop it, the less able they are to take it.
I suppose the first step is to figure out the pathway wherein the Confederacy ends up in Arizona.