Apologies for not responding after my test, I've been quite busy with things going on in life and genuinely forgot about this. I received an email about your comment and here I am.
I took the Rotom-Fan over to Kukui's basement, reverted it into its standard forme, and then changed it back into Rotom-Fan. I went to the Battle Tree to see if it would allow it, and it did. I further tested this by switching it with my Rotom-Heat (this was also transferred from Alpha Sapphire as Rotom-Heat, but I did not change its forme from Kukui), and it allows it as well.
I decided to test out Battle Spot and see if it would allow me to use Rotom-Fan (unfortunately no one is available for a local battle so I can test under the same circumstances). The Battle Spot (free battle, special Pokémon allowed) allowed my Rotom-Fan to be used. Rotom-Heat was also allowed. The results were the same for Ranked Battle Spot. For what I know there were no recent updates for Sun and Moon. I can do a local Link Battle on Thursday (the 16th) so I will see what happens there. I'll post my update later that day.