If you leave the over the fire air controls open you will be reducing the amount of air going through the coal bed.. If you have a marginal chimney with marginal draft, you may have problems keeping the fire going with the air getting in over the fire..
The reason that some stove manuals say to have some over the fire air, is that when fresh coal is added in quantity to a fire, some volitiles burn off the coal at first. These volitiles can ignite all at once..
Here is a thread on this topic: Minor Explosion In Coal Stove