If you burn more than your expected trip fuel, you have your contingency fuel (that's the reason you carry it). If you burn that out, you can choose maybe a different alternate, that is still suitable and requires less fuel. If don't have any, you could maybe decide to cancel your destination alternate as per the regulations in your country and your your ops manual. Anyway that is just theory because whenever you decide that you want to divert it is just your decision, and if you start your diversion above the minimum diverting fuel you probably have all your reasons to do so.
I'll mark that down as a "No."