How to simulate parasitic reactances in a circuit
Parasitic capacitance absolutely adds to the value of a physical capacitor on the same trace (same goes for inductors and resistors!).

In a microstrip the parasitic capacitance is to the shield layer (typically ground).  So that would be a parallel capacitor and would add.

Likewise, the inductance is due to the trace itself (self-inductance) and also might have some mutual with other traces.  It is a series component that adds to the inductance of the trace.

A good rule-of-thumb if you're confused is that parasitics on a signal trace will make matters worse, whether for capacitance, resistance, or inductance.