Oh man, I'd forgotten how interesting the electrical conversations get on the internet.
One potential hazard has been covered well here. Defective equipment (the adapter) could get hot if you use the circuit more (more amps).
I'd check the adapter once in awhile too, but not because I might suck 19.99 amps from a 20 amp circuit. If the thing gets hot, turn off the circuit and throw it away. It is defective if it gets hot, and it is not defective just because you decided to run your AC.
But the other hazard is that MORE than 20 amps may flow through the circuit if the circuit is improperly built.
Personally, I'd look in the panel for a breaker labeled 20 amp. Many people call a circuit "a 20 amp circuit" because it looks like one, even though they could be wired using bigger breaker (a mistake). Blowing the 20 amp breaker is a low risk adventure. Drawing over 20 amps using a circuit with some of the parts designed for 20 amps is a high risk adventure,
