I have a 2010 Equinox that I recently started to dinghy tow.
I will have to check but I don't believe the odometer registers the mileage. In your owners manual should be a procedure to follow for dinghy towing. The procedure involves removing the "discrete logic ignition switch" fuse. This fuse is located in the instrument panel fuse block located on the passenger side panel of the center console. This may stop the recording of mileage during towing.
Sorry I couldn't give you a firm answer.
Good luck,
Bill