They do!  

Perhaps it was a lie none cared about, a small thing…?

Do you want to share more? Love the gossp!

To my knowledge, there was no real background check at BCG in the US; certainly, there was no drug testing even as just about every other company does.

The situation you describe is infuriating. When your 'friend' gets caught though, he will suffer the consequences. Karma works - there will be a day of reckoning

Not surprising at all actually! Quality of talent going to BCG has been on the downhill with them scaling up.

Wonder how the clients will react if they get to know about this

They will check if he attended / graduated from the school he mentions. Not even sure they'll check grades. 

But the past will likely catch up with him, particularly if this so obvious to everyone else in the school. If there are other alumni from that school working for BCG, the word will spread out fast.

Yes, he may get the offer retracted or even get fired for this.