How does radar receive Mode C information?
Correct.  Mode C responses include the pressure altitude.  This means that many installations use a separate altitude encoder that has no barometric settings.

Whether it is integrated or a separate unit, the kollsman setting does not change the pressure altitude reported.

From http://www.faraim.org/aim/aim-4-03-14-133.html


  
  Mode C Veil. [...]  Unless otherwise authorized by ATC, aircraft
  operating within this airspace must be equipped with automatic pressure
  altitude reporting equipment having Mode C capability.