Assuming a dictionary definition, "the feeling or belief that one can have faith in or rely on someone or something", such a feeling or belief rooted in absolutely nothing is just unrealistic. It's still a form of dependence, the only significant difference being that instead of depending on a demonstrable fact, you depend on an unrealistic fantasy. The latter easily breaks down with a simple reality check, unless deeply rooted in religious conviction. Self-confidence without ability is plain arrogance.

Even if you truly don't tie your self-confidence to your abilities, chances are that you judge others by different standards. I don't confide in others on the basis of their bare existence as persons, and I try hard to judge myself by the same standards that I judge others.

The more important concern is choosing which abilities you should hinge your self-confidence to, and learning to appreciate them and judge them fairly.