I don't know anything about the ACOG, never owned one, never mounted one. From what I've seen on the market, the only possible way to do this the way you say would be to use a scout scope mount which clamps on the barrel. That mount is below the line of sight with the irons. I have no idea if the ACOG opening would line up with the sights.
Every other mount I've seen that can also use the sights mounts high above them, so you use the sights below the mount. You would need a cheek riser to use the scope and then you couldn't use the irons like that without removing or lowering the cheek riser.
I have both the scout scope mount and the Bassett picatinny low mount. The Bassett low mount is too low to use the irons, but it's a single retained screw to remove it. It's a fantastic system, it just takes a tiny little wrench that lives in the butt stock to put it on and take it off with a built in torqueing method. It seems to return to zero as good as QD scope rings, maybe better. I wish a mount like this was available for other rifles.