You learn pretty quickly that you can almost never use auto resolve reliably to win anything, unless the enemy have some nasty ability that auto-resolve don't know about.
It's actually quite the opposite, to an easily exploitable extent. If you do the actual battle enemies tend to target the weakest unit, and against ranged units this means your back line squishies are probably going to take a lot of damage, you might even lose a unit or two. Stick a tank in the last slot and they absorb all the attacks in the auto-resolve, no stray shots, no weak units going down in one hit, it's easy mode. Once your tank starts to get low health just move them around and stick another tank in the back while the first one heals, easy levels as you clear the map without downtime. I auto most of my fights.
I have not experienced the mana eating problem, quite the opposite. I've only noticed them using spells a handful of times, which is actually really annoying with a caster sov who ends up hitting things with her staff in most battles. Seems to be only specific spells they cast, I think the only one I've really noticed is Chaos which will be spammed some times, may have seen a champ that spammed burning hands too.