I always thought that the MCC was a precursor to your first Type Rating - but not necessary for the 'fATPL'?
In as much as there is no such thing as a 'fATPL', you are correct. Convention has it that the illusory fATPL comprises a CPL/IR, ATPL theoretical knowledge and MCC (i.e. everything required to commence a MP type rating course and commence line training).