Sometimes yes, sometimes no. I think it is a case by case basis.
In my case I could always tell a hallucination from reality. I also knew that from a clinical point of view my delusion would be considered a false belief. My current pdoc specifically said he was glad I had insight into my illness after talking to him. Nonetheless, it all seemed like this stuff was really happening to me at the time even though no one could hear my voices or see what I saw or felt what I felt or thought what I thought. It’s all gone now since being on meds.
Even when I was psychotic I knew who I was, where I was, what was going on in the world, etc… I wasn’t absent from reality.