I do see that sometimes the sovereigns have 5-10 injuries, so I do know they fight (and not very well). Not sure how much that is monsters or who much that is down to warring other factions.
Can a sovereign take injuries, I only see theyre heroes with injuries, though (im playing on normal) it seems they try to gather all the injuries for some secret acheivement 
On a seeing note, I hope that with the current cost of pioneers that the neutral monsters gets better at defending theyre own home, but also better at attacking pioneers (since my current tactic is just spam pioneers and move them in the direction till some pioneer succeeds the 50% chance not to be attacked (the chance is a guess).
Nice of you mr. frogguy to notice these minor details, havent really paid much attention to this behavior. 
Sincerely
~ Kongdej