Getting therapy is part of the job. Not sure about 'psychology as a discipline' but the therapists I know definitely get therapy and LLM exposure as well.
As I was told by one: the fact that you're able to tell your LLM to be more critical or less critical when you're seeking advice, that in itself means you're psychologically an adult and self-aware. I.e. mostly healthy.
She basically told me I don't look like a dork with my new DIY haircut. (Though I *did" complete CBT so I kinda knew how to use the scissors)
But they work with sick people. And that can mean a range of things depending on that clinical context. Usually sick things.
That said I can’t imagine psychology as a discipline has had time to develop a particularly full understanding of LLMs in a clinical context.