How to check my MBP's logic board properties?
The only way to truly know if something is wrong with any replacement part installed by Apple is based on symptoms of the computer and symptoms alone. Apple does have diagnostic tests they run on each computer that is repaired. That is just a stop gap to find a bad part on the way out the door. Diagnostics will never catch every problem. In other words, if the computer is not exhibiting the symptoms you brought the computer in for to begin with,  the computer (and its logic board ) are fine. 

You can always run the Apple Hardware Test to check for yourself.