If you put +ve to -ve and -ve to +ve then what you are doing is adding the potential differences as they are in the same direction. You are speeding up the rate at which the charge is flowing through the cell and so making it go flat quicker, or other side reactions may occur damaging the battery.
I not entirely sure about this part, anyone else confirm, possibly Mao?
You are partially correct.
The power supply will force the reaction to go in 'discharge' mode. That is correct.
Discharging --> exothermic --> energy is released. In this case, since we're not connected to any external devices, this energy is released as thermal energy. (ever noticed batteries getting hot after use? same idea)
Power supply --> supplying energy --> energy of the system (i.e. the battery) gains energy --> the battery heats up. by a lot. because the wall socket can supply a lot of power.
The end result is both processes end up heating the battery. Which may end up melting it. Some of the chemicals inside the battery may vapourize, and eventually the pressure build-up may cause explosion. Or the battery may run out of reactants, and side reactions start happening, usually resulting in gaseous products and explosion.
(explosions are cool)