No, with the exception of children of holders of an EU passport under the Free Movement Act.
In general all applicants are required to possess an A1 level certificate to join a German citizen, with a few exceptions.
Applicants of visas under the Free Movement Act are not required to possess an A1 level certificate to join EU citizens residing in Germany
The embassy requires substantial evidence, e. g. proof of attendance in language courses for a minimum of 12 months or relevant learning materials if no course was attended.
While you may be fully insured by a national insurance provider in Germany, your family can only be added to your national health scheme after they have been registered in Germany. The submission of a travel health insurance for your family is a requirement for visa issuance to ensure comprehensive coverage for all family members for the travel time until the registration with the national health care provider.