I have seen quite a bit of discussion on whether the cover is for prtection only or whether the rifle was meant to be shot this way.
On my A3 there is no way to shoot with the cover installed. I am using the A sight just to get down to only 6" high at 100yds and the shroud totally blocks the sight picture.
There is a sight hood for the USMC version that is taller and can be left on but good luck finding one for a reasonable price.