When you say grassy slope is it completely grassed over and is it a very large area, given time this cotoneaster will block the weeds and grass coming through, but initially if you have grass already there then this will come through, it has to have time to thicken up, but this is a very quick growing cotoneaster and once growth spreads out ,the tips will root themselves , and so it carry s on basically forming new plants as it goes, would you be able to clear the grass prior to planting, also if its a large slope you maybe better to plant a few to get quicker coverage.

In my experience, the grass will still appear between - I have Cotoneaster Queen of Carpets planted in a garden, good ground cover, been in seven years, but any grass that gets in there (usually couch) still pokes up between the (now dense) plant covering. And its impossible to remove...

Thanks Julien and Bamboo,
I will clear the grass on this small slope, plant the shrub and hope for the best! Presumably if I keep it in check, it will thicken up?