In your case it's indeed better to go with the proposed solution but for the record, yes you can duplicate - in a way - a CALayer : using CAReplicatorLayer.
It's a very powerful API, not necessary build for duplicating one layer but it works for that too. It works even better for making astonishing visual effects by duplicating series of layers.
For more information you can have a look at the apple official documentation, here an extract:
A layer that creates a specified number of copies of its sublayers (the source layer), each copy potentially having geometric, temporal, and color transformations applied to it.
And here a great tutorial by John Sundell, another extract:
CAReplicatorLayer specializes in drawing multiple copies of an original layer (hence it being a "replicator"), in an efficient - hardware accelerated - manner. It's super useful when drawing things like tiled backgrounds, patterns or other things that should be repeated multiple times. I even use it to implement the texture tiling feature of my upcoming open source Swift game engine.
And finally here a great example of what can be done with this api.