Not yet, though Riot's working on one. One of the big complicating factors is that there isn't really a hard line you can draw from champion to champion, as you pointed out with Vi as an example, so there are going to be a lot of hybrids of two, three, maybe even four subclasses. There's also likely a lot that needs to be specified in the model before proceeding with a list, such as a definite table of which features or mechanics correspond to which specific subclass (if a champion has persistent AoE, for example, does that automatically make them a Disruptor?).
I also feel the model Rito proposed needs a bit more work, and making a list based on the current version is likely to lead to very heavy revisions quickly after. It's clear that the marksman class needs to be broken down into subclasses, for example, and the dev blog's description of the Diver subclass also failed to assign them any specific weaknesses or tradeoffs, or any specific mechanics beyond just good back line access, which would likely make far too many champions diver-assassin and possibly diver-skirmisher hybrids. There's also a lot of inconsistency between their model and common jargon that they themselves use to classify champions (i.e. nobody using the "enchanter" qualifier, ever, and using the term "support" when the class doesn't exist as such under the new classification system), and that might also be cause for disagreement when it'll come down to pinning down a few cases (is every champion with an ally-oriented buff an Enchanter? If so, does that mean Ezreal/Fiora/Gangplank/Warwick/etc. have the Enchanter subclass as part of their makeup?).