no, unfortunately the Ausbildungsduldung is issued only for the person who applies for it, under the condition that the person fulfils the requirements. The other family members can only have Ermessensduldung (Duldung in discretionary power of Ausländerbehörde, which can be given on urgent personal or humanitarian reasons - in this case a relation to a family member who will stay for long in Germany with Ausbildungsduldung). The problem is that in many cases the Ausländerbehörden don't want to issue this Ermessensduldung to family members but insist on leaving Germany ("Ausreiseaufforderung"). They argue, for example, that the decision to make an Ausbildung is a personal free choice and the trainee can choose to leave Germany with the family if it is more important for him/her (I saw such letters myself a couple of times).
If you don't have a reliable promise from your Ausländerbehörde to give Duldungen for the whole family, I would recommend the family members to make an official written application for Ermessensduldungen und in case of rejection to make Widerspruch an, if necessary, an urgent application (Eilantrag) in the Administrative Court.
You can be in need to take a good lawyer whe specialises in migration problems. Anyway make contact to a good consulting place.