Ill throw some thoughts down...
The less source images the gpu has to draw from at runtime, the lower the draw calls, the better the performance. People recommend to use a max of 2048 textures because most devices now support that.
However many modern devices also support 4096, so if you know you are deploying to a modern iDevice you may choose to do that in your "HD" version or something.
An iPad pro with a resolution of 2732x2048, has a scenario where you could need a max of 6 source images (draw calls) if using 2048, where 4096 would only need 4.
In your specific case, your "atlas" is always maxed out at one large image. I do not think there would be any reason a texture atlas of one image is more performance than loading one image of the same size. Unless there is some kind of embedded/memory thing im unaware of. Personally I have only loaded image with xml in assetmanager. (Atlas)
The idea of the atlas is to pack as many things in to one image file as you can fit. You however, can only fit one anyway.
The irony is that the modern devices that support 4096x4096 are usually so well performing that you may not visibly detect improvement over lowering the draw calls anyway
If you specifically wanted to make your background images at size 1024, then yes definitely a texture atlas packing them in to fit 4, or 8 on one image atlas and save you draw calls
Also, i have no idea how realistic it is. Sounds like a lot of gpu mem overhead unless you are unloading/loading the images not in use. What about gpu memory left for the rest of the assets? Anyway thats kind of a different discussion
Depending on what you are doing, you might try to pack the images at a lower resolution and scale up at runtime, see what it looks like. This is especially fitting if the background has a blur to it anyway, like some games do. If this works for your use case, you can save quite a bit of memory.
I recently read an interesting take on this at darethemonkey.com where he mentions this, or even scaling only on one axis or the other, both having slightly different results. http://www.darethemonkey.com/2017/02/24/graphics-optimisation-tip-5/