Method actors don't just pretend an emotion (say, despair); they recall experiences that once caused it, and in doing so, they actually feel it again.
By analogy, an LLM's “experience” of an emotion happens during training, not at the moment of generation.
LLMs are definitely actors, but for them to be method actors they would have to actually feel emotions.
As we don't understand what causes us humans to have the qualia of emotions*, we can neither rule in nor rule out that the something in any of these models is a functional analog to whatever it is in our kilogram of spicy cranial electrochemistry that means we're more than just an unfeeling bag of fancy chemicals.
* mechanistically cause qualia, that is; we can point to various chemicals that induce some of our emotional states, or induce them via focused EMPs AKA the "god helmet", but that doesn't explain the mechanism by which qualia are a thing and how/why we are not all just p-zombies