You always have the RIGHT to appeal to the state's intermediate appellate court. That does not imply any chance of it actually having a positive result, outside of an exceedingly narrow set of reasons. Generally, plea bargains are not appealable. The exceptions are few.
Finishing the case in the interests of "judicial economy," among other things, is WHY plea bargains even happen. If any retard (and by "retard" I mean "Nick") can just take a plea and then have second thoughts, there wouldn't be much point in having them, now, would there?