Do these watchdogs reset the circuit or jump to some vector to service the watchdog?

They actually generate a hardware reset and even pull the reset pin high to reset external circuitry.

Also, I noticed that sometimes on noisy power supplies the uC hardware itself hangs (even the ALE is flat). This seems to indicate that the internal clock and other circuitry itself is not running. I am pretty sure when this happens, its not good for the micro :-)) - but how common is this? Are the internal watchdogs so independent of the rest of the uC that they can break out of such a scenario too?
I do believe that the internal watchdog is depending on the clock only. A reset will disable it, but a reset from any source would not be any different than a watchdog reset.

Erik