Can USB Type-C 2.0 upstream (device) connect its CC pins and share a pull-down?
No, the CC pins should not be tied together on Type-C receptacle. USB Type-C specifications, V1.4, has several places that deal with use of CC1 and CC2 pins. 

If you are making a USb 3.x implementation, the active CC pin will tell you the right direction of Rx/Tx data MUX. Individual CC inputs on device receptacle form the entire idea of detection of plug orientation. The specs describe the process on p.165, Section 4.5.2.2.5.1 as:


  If the port needs to determine the orientation of the connector, it
  shall do so only upon entry to this state by detecting which of the
  CC1 or CC2 pins is connected through the cable (i.e., the CC pin that
  is in the SNK.Rp state).


More, on pages 162 and 163 the specs explicitly say, i.e. Section 4.5.2.2.3.1:


  Both CC1 and CC2 pins shall be independently terminated to ground
  through Rd.


Is this enough to convince you that CC pins should not be tied together?