Hey there,
Agree with Ian. You need to have a certain level of casing skill to benefit fully from such sessions. While in general, their feedback will always be somewhat generic (''work on your structuring, generate more tangible insights, etc.''), since they cannot spill the secret sauce + are usually not trained as interviewers, their feedback will be more targeted if you give them a better performance to work with. To get the secret sauce, you need to work with a former consultant as a coach who can do that...
Generally, your performance in these interviews is never communicated to HR or anyone else in the recruiting process. It is really just a nice offer to help you prepare and point you in the right direction. Also for McKinsey, consultants who conduct these coaching calls are usually also not part of the actual interviewer group. Not sure about BCG but might be similar.
Cheers,
Florian