It is quite easy to determine if a CMM can actually measure your gear or not.
1. Check, what quality class of gear you want to inspect.
2. Check, which profile form and flank form tolerances this quality class has.
3. The R-Spec of the CMM (Its Form error according to ISO 10-360-2) should be 20% or less of this tolerance. Only then your CMM is capable of doing the job, no matter what the salespeople say.
Example: Your gear is class 5 (DIN 3962)
Class 5 means its permitted flank line form tolerance is 4.5µm. ==> The CMM form error (R) should be 0.9µm or less.
Only CMM's with a high precision measuring probe head are capable of gear inspection. All the rest is nonsense.