A mutual insurer engaged in no activities other than those specified in s. 616.06 may apply to the commissioner for designation as a school benefit insurer. If the commissioner finds that the insurer is engaged in no other activities, the commissioner shall declare it to be a school benefit insurer. As long as the insurer’s activities are thus restricted and it uses the term “school benefit” or its equivalent in its name, it is deemed to be operating under this subchapter, within the meaning of s. 601.31 (2) and shall have the tax exemptions under s. 616.10.