Often yes. Some routes clearly require the insured person to hold a valid visa for the full duration of the period of insurance.
This is not just an immigration question. It can also affect eligibility under the cover itself. If the visa expires, is revoked, or does not match the insured period, the support or claims outcome may be affected.
If your visa timing is uncertain, do not wait until later. It is better to clarify the issue early than to discover a mismatch after a problem arises.