Yes, we are.
Wikipedia defines self-awareness as "the capacity for introspection and the ability to recognize oneself as an individual separate from the environment and other individuals". At a minimum, this would require GPT-2 to have a model of the world which included a representation of itself. To be similar to our intuitive understanding of self-awareness, that representation would also need to guide its decision-making and thought in some significant way.
Here is an intuitive explanation of the Transformer architecture that GPT-2 is based on. You can see from the explanation that it's only modeling language; there's no self-representation involved.
Technically, I guess you could say that, if a Transformer architecture was trained on texts which talked about Transformer architectures, it would get a model which did include a representation of itself. But that would be just another data token, which the system gave no special significance to, and which wouldn't guide its behavior any more than any other piece of data.