What happens if usage current exceeds DC adapter current rating?
Best-case scenario, the adapter has a foldback circuit, which causes it to drop the output voltage substantially and shut down your attached equipment. This is unlikely unless you've specifically bought and paid for an adapter with this added feature.

Worst-case scenario, the adapter heats up until it catches fire and burns your house down.

Likely scenario, the adapter runs very hot and eventually fails, after years, months, or days, with or without damaging your attached load.