Sure. There are an increasing number of roses in that group.
But before you plunge into them, consider your existing terrain.
We have a rough hillside, and some of it is covered with appalling ice plant. That's nasty stuff to start with, but consider your ground cover roses, and how you will handle weed-growth from up under them.

Jeri

Which one you choose is up to you, however, consider how awful cleaning the weeds and rubbish from that hillside is going to be with something prickly! If you can come up with one that is thornless, you'll be MUCH happier!

You can literally use any rose for "ground cover". Trailing, rambling or even climbing roses can be allowed to just grow as they will and they will "cover" a hill or field. It's going to take quite a while for any of them to get dense enough to prevent weeds from penetrating through them. Often, lower growing bushes, such as polyanthas, are used to cover beds in mass plantings. Though for that use they aren't called ground covers, they are. The only difference is on a hill side, you most often don't consider it a "bed" as you would around your driveway or up your front walk.

If there are paths across the hill, you could use a bush like Iceberg, or other heavily flowering variety that doesn't require constant dead heading to keep flowering. If it doesn't have to be repeat flowering, there are thornless species and species hybrids, such as Basye's Thornless Wichurana. It flowers in spring with single, white blooms. The remainder of the year it is just green. Kim

I think you may have to steel yourself to the idea of at least occasional maintenance, as I've never seen a rose that could smother everything that tried to come up beneath it. However, I'm not familiar with the ground cover roses. Our ground is steep clay, every bit of it. We have a one section that is very steep indeed: we terraced it with boards and rebar, backfilled with some extra dirt, and planted a variety of roses, mostly Teas. Now that the roses are established we don't do much of anything to them. My husband recently scrambled down (or up, I forget which) to pull a sucker from the grafted 'Mutabilis', and we've been throwing down the litter from the rabbit's cage to feed them, but that's about all. I mention this situation in particular as it is a place that's steep enough to make access a matter of climbing, yet the roses do reasonably well. Do the roses have to be low growing? You would want something that doesn't need much pruning or deadheading.
Melissa

Daylilies, Ajuga, sedum are three ground covers that work better for me than roses. I love roses, but clearing weeds from beneath those thorns is a daunting task to say the least.

There are many many more ground covers from which to choose.

Just my 2 cents.

Barbara

There are miles of highway in California lined with piles of R. banksiae lutea (yellow Lady Banks). No thorns. Great display in the spring.

Everybody that I know who has tried a thorny "groundcover rose" has ended up cursing it. Maintaining it isn't terribly hard, since you can shear it, but getting at weeds and trash is a problem, as is picking out cut canes.
Anita

Or, if you're in an area with higher summer heat, plant Purezza. Regular Banksiae will flower much of the summer where it's quite coastal. There, the 'spring weather' continues most of the summer until later fall and they flower as long as they "think" it's spring. If your area gets HOT, I mean in the nineties and above, earlier than say, September, Purezza will flower as long as it is HOT. Neither present cleanup problems as neither have flesh ripping prickles and both are rudely healthy in most places. Purezza only comes in white. Traditional Banksiae comes in double and single white as well as buttery yellow.

You can shear it as Anita says. I know of several landscape companies which machete it and the plants THRIVE. Kim

One really funny sight -- On Hwy. 101, in Paso Robles, they've planted lots of R. banksia lutea, among trees, and other shrubs.
On the Southbound side, the banksias quickly found the little pine trees, and began "climbing" up them. The poor little trees were only maybe 5 ft. tall, so now they are just pyramidal mounds of R. banksia lutea.

That said, I think Kim's right. In the right climate zones, the banksiaes would be perfect for this job, AS LONG AS YOU DON'T HAVE DETERMINED WEEDS COMING UP UNDER THEM.

Jeri

You know, Jeri, even determined weeds wouldn't be that much of an issue with Banksiae. You can pull a pile of weeds from things that don't make you BLEED! Kim

Kim, if we had a hillside covered with Banksiae, it would have to be preferrable to the @#$$#$#@@@#$$% Ice Plant that covers it at present.
I hasten to add that while we've made many mistakes in planting, we INHERITED the ice plant.
If I ever win the lottery, I will hire an army of guys with strong backs to strip that stuff from the hillside, permanently.

Jeri

That bloody iceplant grew here for years, then died out. In front and in spots in back, it's seeding itself! I amazed just how water thrifty Banksiae can be once established. Give them rains with good water penetration and they make it on their own. Kim

I don't know to what extent this depends on a good annual rainfall--which we have--but old roses at least go through summer drought without batting a petal. A few years ago we had four and a half months with a centimeter of rain for all precipitation, and the roses did fine. We gave no supplementary water. Having heavy soil helps, I imagine.
Melissa

I am considering planting an Awakening to cover the downside of my "garden" in potting soil quality dirt (was my former horse manure dump site). I am in love with its parent New Dawn but might chicken out and send it up the trellis instead with an Eden.

Are you in California, HU? I bet Awakening would be lovely there.