Short answer: No. Life insurance paid because of the insured’s death is excluded from the beneficiary’s gross income, whether the employer or the employee paid the premiums. Interest earned when proceeds are paid out over time later is a separate matter and can be taxable.
Federal law excludes from gross income amounts received under a life insurance contract, in a lump sum or otherwise, when paid by reason of the insured’s death. The tax treatment of the premiums during the employee’s life, including any imputed income, does not change that.
The exceptions are narrow. When proceeds are held and paid at a later date, the part representing interest can be taxable, and a policy that was sold or transferred for value loses part of the exclusion, which almost never happens with group coverage.
In Texas, the policy must pay the designated beneficiary, though it may reserve the right to pay up to $250 to a person who paid funeral or last-illness expenses. Keep beneficiary designations current; that, not tax, is where group life claims usually go wrong.