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).

An electric pressure cooker actively senses pressure (generally through the deformation of the pot), energising the heating element only when the pressure drops. So while it definitely boils while being heated, the majority of the time it's not actively boiling, just at boiling temperature.

As for whether that will "baste" an object inside the pressure cooker: No, but that doesn't matter. The relative humidity in the pressure cooker is 100%; pouring liquid over the object won't have any effect on how moist that object is (not that basting has much effect on the moistness of meat in any case).

At 12 psi, water boils at 243.7F. That said, it would be difficult to maintain a rolling boil.

The rolling boil is easiest to establish in an open or well vented pot where water vapor can escape as fast as it is produced. In a fully closed pot, adding heat raises the temperature, which increases the pressure, which raises the boiling point and in effect inhibits boiling. The pressure cooler, with a safety valve, is intermediate to these two extremes. Even so, the heat required for a rolling boil would still have to be in excess of what is needed to maintain the elevated temperature and pressure plus lift the valve plus replace the heat carried away by the super heated water vapor. We can see that maintaining a rolling boil in the pressure cooker is going to be challenging compared to an open pot.

There are a few concepts that help us understand what is happening in a little more detail.

Vapor pressure - is the pressure exerted by a vapor in equilibrium with its condensed phase. Vapor pressure generally increases with temperature.

Partial pressure - the pressure above the liquid in the closed pot, has a contribution called the partial pressure, from each component in the gas phase. The partial pressure due to the liquid in the pressure cooker, is identically its vapor pressure.

Boiling occurs when the vapor pressure is equal to (or exceeds) the pressure in the environment, the ambient pressure.

Equilibrium - occurs when opposing processes are in balance. Examples can include evaporation and condensation to establish a vapor pressure, or heating and cooling to establish a temperature.

With that preamble, lets consider what happens in an open pot compared to what is happening in a pressure cooking.

In an open pot, pressure above the liquid remains close to that of the surrounding air. Once it reaches the "boiling point", adding more heat results in more steam being produced which then carries away more heat and so the temperature stays close to the boiling point. Adding enough heat, can bring us to a fast rolling boil.

In a pressure cooker, we have a closed pot (up to some pressure where the vale opens), and the steam cannot escape to carry away the heat. Even before we reach a boil, adding heat increases the temperature and thus increases pressure inside the vessel and thus increases the temperature needed to reach boiling. Over this range, boiling in effect is self attenuating and energy is stored in the increased pressure.

If pressure becomes sufficient to open the valve, boiling might pick up from that point, but holding the valve open becomes part of the energy budget along with the extra heat carried away in the super heated water vapor and again, it is energetically expensive to maintain a rolling boil.