I want to know if there is a practical way to find out if multipath propagation is significant for audio in a given environment?
Never done this but it might work. Record the audio simultaneously using multiple microphones located in the neighborhood of your main recording position. If the cross-correlations between signals from different pairs of microphones show peaks at different time lags than the autocorrelation, then there must be either multiple sources or multiple paths. Be careful not to confuse multiple paths with reflections from the microphone bodies.