anti-alias filter of square pulses
From an ADC perspective, it is just taking a sample of the voltage in time. I fail to see how a "misinterpretation" could be made since there is no "turning car wheel" to take pictures of at the wrong time. Do the harmonics alias in such a way that the wave shape is preserved?


You can reason this out yourself, in the time domain.  Consider a square wave with values -1 and 1; and sample it at exactly five times its period.  You'll get something like {+1, +1, -1, -1, -1, +1, +1 ...}.

If you just have to think about this in the frequency domain, you can, after a great deal of work, demonstrate to yourself that not only do the harmonics not alias in a way that preserve the shape, but in fact alias in a way that does not preserve the shape -- you end up with edges aligned with the ADC sample points.


  In my mind, adding a filter to the signal will modify the shape of the original signal, getting rid of those upper harmonics. Depending on the filter design, it could add overshoot, ripple, and/or rise/fall time changes. So wouldn't the best representation of the pulse be obtained by direct sampling?


That depends on what you're trying to do.  If your goal is to accurately capture the timing of the edges, to something less than the ADC sampling interval, then you need to round those edges out -- because a signal that goes {+1, +1, -1, -1} has less information about the location of the edge than one that goes, e.g. {+1, 0.75, -0.25, -1} or {+1, 0, -1, -1}.

And finally:


  I'm trying to determine whether or not an anti-alias filter is needed for sampling square waves.


That depends entirely on your problem at hand.  If you need every bit of information contained in the wave (and not just its timing), and if it truly has energy content out to infinity (which is physically impossible) then you need to sample infinitely fast.  If you know it's bandlimited, then you know the sampling rate you need to use.  If you know that, for example, the edges are super-sharp but what you really care about is their timing, then you can filter and acquire with an ADC, and infer the actual position of the edges from the way that the measured "square-ish" wave transitions.