It is not part of the fishless cycle.
There are several fungi that it could be. Mostly these would be a gooey slime or fuzzy. I would wipe it off so it does not get to be too much, but do not tear down the set up. Just keep cleaning it.
If you have hard water sometimes certain minerals can come out of the water, and you can see a white film or white deposits. This would not build up as much or as fast as fungus could grow. While it will likely be somewhat softer as long as it is wet, it will get hard and crusty on any part that dries out. To understand how plants can do this look up "biogenic decalcification".