Psychiatric disorders, in general, are not covered under health insurance schemes in India. However, since there are a large number of insurance companies now, it is possible, that some company might have a policy providing some sort of such cover. Under the circumstances, no data are readily available.
However, you would appreciate that even if such cover might be available in theory, the company is likely to deny payment on the ground that it was a pre-existing disease or condition. It would be extremely difficult to prove that a psychiatric disorder was not pre-existing.
It is rare for insurance companies to cover suicidal death due to whatever cause.