I want to know if there is a practical way to find out if multipath propagation is significant for audio in a given environment? I am employing audio signals generated by a mechanical press for Blind Signal Separation. But, prior to algorithm application, I need to clarify if the signal strengths coming in multipath (except direct path) are significant.

Ideally, I would like to use the four microphone recordings of audio generated by this press for this task. However, if it's difficult or impractical I am interested in trying out other methods.

Cheers!
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.