My experience is with military radios, but I assume civil radios also continuously monitor guard (in addition to the active frequency) unless guard is toggled off.
No, unfortunately not - the second radio needs to be tuned to the frequency.
As far as the "guard police" go, in UK on 121.5 it's usually airline pilots getting it wrong, due to finger trouble when trying to call handling agents.
The other annoying ones are those calling up to request a "Practice Pan" in advance of the actual call. If they just listened out then made the actual call it would require two fewer calls! If it's inconvenient then London Centre would tell them so and they could desist until another time.
Having said all that, it's hardly rocket science, if 121.5 is deselected due to distraction, to remember to turn it on/up again. I manage to do it single pilot I monitor 121.5 even though I'm not actually required to do so in Class G, where I spend most of my airborne time.