Here we go again, perpetuating the myth of the 'Frozen ATPL'. The so-called 'frozen ATPL' is nothing more than a CPL/IR, the only difference is that the ATP theoretical knowledge exams have been passed, which, along with the MCC course, are a pre-requisite to add a multi-crew type to the CPL.
If the PPL in question gains a CPL/IR and passes the CPL theoretical knowledge exams he can act as pilot in command of an aircraft certified for single pilot operation for any purpose, including commercial air transportation. If, on the other hand, he passes the ATP theoretical knowledge exams he can, in addition, act as co-pilot of an aircraft certified for multi-pilot operation.