Should the times series be made stationary before doing a clustering analysis?
Not sure, but I don't know any task related to time series algorithms and analysis for which it wouldn't be useful to make the time series stationary first. You simply get rid of a lot of unexplainable anomalies this way.
Maybe only if you use several different time serieses of the same period, then one could try to find some usefulness in comparing the unstationary serieses.
The effects of the unstationary series, are not explainable by the same series alone.