Do you mean, do they attack units nearby?  The answer is yes.

Do you mean, do they attack cities and outposts?  The answer is a qualified yes, both for the AI and player.  Neutral monsters will sleep, roam, and attack, which means they may seem to be doing nothing, and then suddenly decide to attack whatever is near them.  Some roam further than others, and some hug their lairs, so there's no exact, single method of predicting behavior.

Auboy, are you by any chance playing "Tarth" or a race with "Master Scouts", since they have a special ability to hide from creatures, and that might change it a bit.

Jaosoze, I'm a bit worried too, but I have faith

Sincerely
~ Kongdej

From the games I've played it takes time before the monsters go on the rampage and kill cities. I'm not sure what turn it is, but a time will come when creatures will no longer tolerate encroachment on their land. Usually what happens is that lairs spawn monsters to roam around every so often and when that happens chomp chomp... a message saying an AI is out of the game, or you are scrambling to defend your weakly defended city from an angry monster.

I don't think they will lose this mechanic as this is what makes this game extremely fun to play.

It is certainly frustrating that the AI spams like its going out of style and cares not if some potential huge, devastating monster is 1 to 2 tiles away.  Then said monster just yawns turn after turn after turn.. then wanders into my territory.  This bugs the crap (_understatement_ ) out of me.