Unless the cover has a bee space recess, ants (and other insects) will move into the cover/inner cover space.
Adding the binding frame with beespace and an access hole, the bees will patrol the space and keep ants away. There may be a little bit of bur comb built in the 3/8th space, but not enough to worry much about. Using a small recess on the super side prevents a lot of bridging and bur but does crush as many bees when replacing the cover. Leaves a 1/8 + 1/8th = 1/4 space on top of the frames.