It's one of those "it depends" answers. Nitrate can be removed form the system by water changes, conversion and use by plants (they convert lots of nitrate/nitrite over time), and by anaerobic processes. This last process involves an anaerobic process converting the nitrate to gas and can be summarized by: NO3- NO2- NO N2O N2
Note this conversion to a gas requires anaerobic bacteria. Is it possible to get anaerobic conditions in the "pores" of the media? If so, many denitrifying bacteria are facultative anaerobes, which means they can break down both nitrates and nitrites, depending on oxygen levels. Since anaerobic conditions aren't optimal for aquaria, we normally use plants or water changes to get rid of nitrate.
This does get to something I've see mentioned in passing regarding substrates - since "complete" denitrification occurs only under anaerobic circumstances, denitrification can occur in deeper areas of a tank's substrate, thus supporting the idea that there is a benefit to small
anaerobic areas in substrates.
Back to the original question - unless something in the Matrix produces anaerobic conditions (perhaps within the porous media itself?), I don't see how it removes nitrates.