if you cover couch grass you can slow it down and stop it taking over your plot so quickly. it doesn't kill it but it does weaken it. I've got a few bits of carpet and some black weed membrane on parts of my plot, and when I peeked under it the other day the bindweed, nettles and couch grass were still there but very pale and definitely struggling ;D
but it will still be alive and you'll have to either dig it out or treat it with chemicals... up to you!
good luck :)