I checked on cloud, and found that yes this looks like a bug, not necessarily limited to one plot function. I also tried parametric plotting:

(*As clear as clear Space!*)
PCF = Quantity[PixelClock[Quantity[20, "Microseconds"], 
   Quantity[1, "Microseconds"]][#],"Volts"]&;
ParametricPlot[{Quantity[t, "Microseconds"], 
PCF@Quantity[t, "Microseconds"]}, {t, 0, 40},
Axes->False]

Documentation for plot explicitly allows quantity. No reason that parametric plot should behave any differently with input {t,F[t]}. The returns I got from that call was blank? Nice find, but my preference for simplicity would just always leave the plot parameter dimensionless, as it is in V.I. Arnold's math phys. theory. Here's another way to write the function & graph, assuming channel saturation at 1V:

PCF2 = ReplaceAll[Plus[SquareWave[{0, 1}, #/20],
     SquareWave[{1, 0}, #/20 + 2/20]], x_ /; x > 1 :> 1] &;
ParametricPlot[{t, PCF2[t]}, {t, 0, 50}, AxesLabel -> {"ms", "V"}]
Plot[PCF2[t], {t, 0, 50}, AxesLabel -> {"ms", "V"}]

The parametric plot is much more concerning, because I would think that expression is closer to what the output of an oscilloscope looks like (except without knobs to cycle units). Quantities are useful when doing conversions, but even then, my preferred method doesn't work in WL, for example:

Convert["Seconds,", "Milliseconds", val_] := Times[val,
  Divide[Quantity[1000, "Milliseconds"],
   Quantity[1, "Seconds"]]]
Convert["Seconds,", "Milliseconds", Quantity[1, "Seconds"]]
Out[]:=1s