The answer is no. People with hypochondria, or illness anxiety disorder, have persistent worries that they may have a serious medical illness. They are not concerned about having a mental illness. But hypochondria, or illness anxiety disorder, is a mental illness, and people with hypochondria truly believe they have a serious medical illness that the doctors and tests have not yet detected.
Hypochondria, or illness anxiety disorder, does co-occur with other anxiety disorders such as GAD (generalized anxiety disorder), panic disorder, and OCD (obsessive compulsive disorder). It also co-occurs with depression (APA, 2013).
References:
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Arlington, VA: American Psychiatric Publishing.