This is part of the "Everything Nodes" development of Blender that should come in 2018 hopefully. They want to do it really really well.
Right now most full time developers are concerned with the new amazing viewport, PBR Realtime, GUI changes for better workflow in production pipeline, rewriting the Dependency Graph (utterly important for Everything Nodes later on btw) and many other goodies coming in 2.8 over the summer/autumn of 2017.
However, you can bake this! Unfortunately it won't be realtime and you can't animate it. Once you get everything set up it should be pretty fast to update.
Plug your noise into Diffuse BSDF, create a non-overlapping UV Map and then bake the Diffuse Color, then save the result and load it as an Image that uses the baked UVs. I won't go into detail on how to bake but all of these steps should take only about a minute once you know what you are doing. No realtime update though.
How to Bake: https://realfood.tesco.com/baking.html
How to really Bake ^_^: https://www.blender.org/manual/ko/render/cycles/baking.html
Tip: If you are only using a plane and not very complicated geometry, I recommend doing all of this through a camera and not baking it. So you capture the animation from above with Emission Shader set at Strength 1 and then load it up as a Movie (or maybe Image Sequence).