If you exceed 500 mA of current draw, then the result is going to be highly dependent on the exact implementation of the source current limiting.
It is possible that there will be no current limiting and you will have no issues at all. It is possible that there will be a PTC or similar electronic fuse. This will likely allow you to draw over the limit for brief periods. It is also possible to have a hard current limit that will either drop the voltage to clamp the current, or it will trip and disconnect the input voltage entirely.
The proper solution is to add enough capacitance so the transient over 500 mA will be supplied by the capacitors instead of the source. It might be a good idea to add some sort of current limiting to the power rail to make absolutely sure your device does not exceed 500 mA. A small-value resistor may be sufficient. Or you may need to turn to some sort of active current limit circuit. Something like a PTC will not be fast enough to prevent an external current limit from tripping.