If you are talking about a plug rated at 20 A and not that the
device it is attached to as drawing 20 A then nothing will happen
unless the device along with other devices on the same circuit trip
the breaker.
The rating of 20 A on a plug tells you the maximum current that
should go through the plug. The 15 A breaker protecting the outlet
ensures that no more than 15 A can go through your 20A plug.