I am guessing that you could estimate this. Make a file with a bunch of test tones at a variety of frequencies, and feed it into your recorder, once with the HPF and once without. Then look at the dB difference at each frequency; maybe a plot would make it easier to see. Using the difference should account for any baseline non-linearity in frequency response. The graph should be flat above the corner frequency and sloped below. I think that for the sloped part to be a straight line, the graph would have to be plotted such that each interval along the frequency axis corresponded to a halving of the frequency. The intersection of the flat and sloped parts of the graph should be the corner frequency.
All of that's assuming that the rolloff is a sufficiently linear number of dB per octave. By selecting additional frequencies to test, you could refine your estimate of the corner frequency.
I think...I might be wrong about the whole thing, though!
If I am, maybe one of the gurus can help us (I am interested in figuring this out, too)...