I’ve done it a couple of times by accident (getting a better price and forgetting to cancel original booking). Nothing happened. The error is usually because of the way National displays (or not) reservations which is irritating. Even when one clicks on “all upcoming trips), if there are several bookings sometimes they don’t all show. Someone up thread suggested if this habitual then one might have a problem. Makes sense.
I had a situation a couple of years ago with an airport reservation (National) and an in-town booking (Enterprise). The latter called 3 days before to confirm (left vmail). They were to have picked me up at home. Despite multiple attempts to reach the local office as well as getting a message sent via central res, not successful. I was a no-show. So much for customer service.