Hey @jbabraham88, interesting question. Psychologically speaking, your definition of a delusion is correct. I would also add the following for further clarification:
A delusion is a belief that is clearly false and that indicates an abnormality in the affected person’s content of thought. The false belief is not accounted for by the person’s cultural or religious background or his or her level of intelligence. The key feature of a delusion is the degree to which the person is convinced that the belief is true. A person with a delusion will hold firmly to the belief regardless of evidence to the contrary. Delusions can be difficult to distinguish from overvalued ideas, which are unreasonable ideas that a person holds, but the affected person has at least some level of doubt as to its truthfulness. A person with a delusion is absolutely convinced that the delusion is real. (Kiran, C., & Chaudhury, S. (2009). Understanding delusions. Industrial psychiatry journal, 18 (1), 3–18. doi:10.4103/0972-6748.57851)
One can make a solid argument that YEC beliefs are indeed delusional. However, there’s an important distinction that needs to be made - having a delusional belief is not an automatic qualifier for a clinical-level diagnosis of “mental illness.” In fact, many people hold some delusional thought at some point in their lives. Without delving too much into the psychology behind it, sometimes the human brain utilizes delusions to preserve mental health and sense of well-being, shielding the person from potentially ego-damaging information.
So to answer your question, in my humble opinion - YECs are delusional, but they are not mentally ill. But then again, I’m delusional at times, so take that as you will! 