How much do max current specs matter on VCC and GND?
It is never OK to exceed an 'absolute max' spec on a chip and expect the chip to function normally.  That particular spec exists precisely because it is possible to draw very large currents on the Vcc or Gnd pin while staying within the individual spec for all of the other I/O pins.  The die inside the microcontroller is sort of a circuit board in its own right.  The pins are connected to the die with very thin bond wires.  These wires and the traces on the metal layers of the die itself are very small and can only carry so much current.  If you try to draw too much current, it will cause the voltage on the die to droop.  The direct result of this could be undesired behavior, resets, etc.  The resistance of the bondwire and traces that cause the voltage drop will also produce heat that can cause issues, up to and including damaging the bondwire and/or die.  

If you really need to supply that much current, you should use external power transistors and/or port multipliers to take the load off of the microcontroller I/O pins and internal power distribution network.