i'm not sure how the cdos r trained in these days 
but during my days, if things r as what u mentioned, we'll be
screwed up-side-down... 
actually we over run n clear the enemy the same way as what the
infantry guys does, except that we do it with the element of
surprised attack, speed and suppressive fire.
fire movement, flanking, taking cover, r the part of key element of
assess during a mission. u will kana screw if u charge / run across
an open, uncleared area.
we've even done live firing with flanking, at night... image, if u
r the one doing flanking, n just before u lob a grenade n charged
at the target, u can see the tracers flying just 5 meters infront
of u, fired from those providing suppressive fire at the target.
by than, even for the stupidest guy in the world will know what's
call "TAKE COVER" 
but i don't think they allow these type of movements nows-a-day
