Is it possible I can save the generated noise in Houdini as a displacement or height map so that I can use it as a alpha mask in Zbrush and Substance Painter?

Sure, if your noise is created at the VOP/VEX level simply apply the texture to a grid and render the grid from top view camera.

If your noise is inside a COP network just drop down a ROP File Output and you can write the comp to a file or sequence on the disk. You can also fetch SOP values into a COP network and export that way too.

Hi Enivob, thank you so much