CRV is crazy popular as toad, right up with Wrangler.
BUT not the Late Model ones! After about 2014, Honda went to CVT instead of a real transmission and the CVT version is not flat towable.
Up to about 2014, flat towable in both the FWD and AWD versions.
Can't confirm/deny if towed miles are recorded. In theory, no, not since cars went away from mechanical speedometers and cables. But, probably depends on what gets energized when the Key is in ACC (if it needs to be, doesn't on all cars) for towing.