If you have one, I suppose it wouldn’t hurt to try (if you can make it fit between the module and light connection — not the whole thing or fan connection, of course), but I’d be surprised since unlike the LZW31/31-SN dimmers, this one necessarily has a neutral wire and the bypass was recommended to solve a specific issue with no-neutral setups on the dimmers. That being said, I don’t know about the particular switch/dimmer used in this module, but some do trickle a bit of power through the load, even when “off”, which might cause flickering or a lit bulb for small loads like this one seems to be…I can’t remember if it was a Zooz or Inovelli switch where I saw this with a closet fluorescent fixture. So it’s not totally out of the question if my experience means anything.
I’m guessing the bulb included with the fan is a no-name bulb, and I can’t find specs on whether it’s dimmable from casual Googling. If you replace the bulb with one that you know is dimmable and preferably specifically compatible with TRIAC dimmers, you might have better luck without needing to worry about any of the above. This is all assuming you didn’t do something like switch any of the canopy wiring, where none of this would help. 
You may also be interested in this new thread (and the support article it links to): Compatible Bulbs/Fans for Fan & Light Switch