Do liquids continue to "boil" when full-pressure cooking is reached?
For as long as it is plugged in and the power setting is appropriate, it should keep boiling as if it was in a normal pot. Imagine if you were to take a normal pot deep underground where you get the same atmospheric pressure and watch it boil, it would look the same as boiling as sea level.

It is the water vapor that sustains the higher-than-outside pressure inside the pot. The lid has a valve that impedes the release of vapor. So, without continuous boiling, pressure would decline gradually (like once you turn off the pot).