Capacitance in serial communication
I think you answered the question already :) Capacitances will influence your communication system in two ways:


Parasitic capacitances: Influences the frequency behaviour(more specifically, the cutoff frequency) of your communication system and if you are unlucky it will do this in the bandwidth of your system, so your signal will be partially filtered/weakened. 
Capacitance of the transmission line: In high frequency communication, the data line and ground will form a transmission line, which indeed, as you stated, has a per length capacitance, but also inductance, resistance and conductance. These determine the characteristic impedance. Mismatch between the characteristic impedance of the communication line and impedance at the load, will cause reflections that distort the data. 


So yes, The per length capacitance influences the characteristic impedance and thus signal integrity. Parasitic capacitance in other places of the circuit in the communication system will influence the cutoff frequency of the system and can weaken the data signal if this frequency is within your bandwidth.