Would it be possible to use artificial grass as a backdrop?

You sure can, like how some people use carpet as a backdrop. Artificial grass and carpet have so many similarities and people even call artificial turf outdoor carpet sometimes. so a lot of carpet applications will work just fine with artificial grass, in your case, as a backdrop. I would like to make one suggestion when you are using artificial grass as backdrop: you want to go with turf with no brown thatching in it. Once you hang the turf vertically, you literally see through the entire thing: artificial turf with brown thatch is best to simulate real grass when installed flat on the ground and the visual effects of brown thatch make it realistic, this is not necessarily true when you hang the grass vertically. So to choose some of product with only green thatch will work the best for a back drop application, here is an example product you can consider: 

https://www.globalsynturf.com/products/trainers-turf-63

To see an application with turf installed vertically:

https://www.globalsynturf.com/photos/roof-patio-deck-artificial-grass-installation-oakland-california/?page=41