it may be possible. You must be 17 when the German embassy and the Ausländerbehörde decide on the application for a visa. The date of the application is not relevant. There are possibilities to enforce a fast treatment by court applications in case you have the impression that your case is not handled fast on purpose.
But you should keep the following in mind:
- Only your parents are allowed to apply for a visa for family reunion. Sisters/brothers can only apply once your parents are in Germany with a residence permit.
- The visa/residence permit of your parents expires on the date you turn 18; they will have no automatic right to stay on further, they will need a different ground to apply for residence permit. (They may be granted a residence permit due to their status as parents only if they are too old and in need of care by you.) So it is questionable whether they can stay on.