Does dual wielding have any effect?
It seems that there is no real benefit from doing this, unfortunately - it would be a great skill for a rogue to have (perhaps as an unlockable skill, like attacking from the back row).
Like you say, when you use either weapon the cooldown affects both hands, so you cannot then attack with your second weapon. On a couple of threads I've found (here and here - the latter on Grimrock.net) there are references to the devs (Almost Human) specifically saying that there is currently no dual-wielding in the game, but I can't find the original source.