Yes you can overcook braised beef so always keep an eye on the braised beef while it's cooking it.
Depending on the amount of braised beef you're cooking it takes around 1 to 5 hours to braise the beef and if you braise the braised beef longer than 5 hours then the braised beef can be overcooked.
The moist cooking method that cooks the braised beef helps prevent the possibility of overcooking the braised beef as long as you do not cook it longer than it really needs to be cooked.
So as long as you make sure to time the cooking of the braised beef and keep an eye on it you should not overcook it.