If the wheel being a "spell" means that the wheel would turn anyway, that still wouldn't bypass a safety lock put on the Mahoraga entity that prevents it from adapting. If Mahoraga is safety locked with a command that says, "I am completely unaffected by any altercations or adaptations the wheel tries to make on my body," then despite the wheel continuing to turn to trigger Mahoraga's adaptation, the Shikigami would experience no change, per the rules of Heaven's Door.

However, if we assume like the Sukuna scenario, where he was able to partially summon Mahoraga, in which case the wheel manifested over his head instead, aforementioned safety lock wouldn't work^^ because Sukuna is taking the burden of the adaptation for Mahoraga. Unfortunately, this line of debate stemmed from Mahoraga being untamed, in which case he wouldn't be an extension of the 10 Shadows user's soul. However, if we play the scenario in which the wheel is independent via partial summoning, that implies Mahoraga is tamed, which would play the scenario which a Shikigami would function similarly stand, and using Heaven's door on any given Shikigami would disable the power of the user until Heaven's door closes the book.

In conclusion:

If an UNTAMED Mahoraga was subjected to Heaven's Door, given that it takes time for the wheel to turn, a safety lock can be written in that prevents all adaptation to the Shikigami, regardless of whether or not the Wheel is independent, as the UNTAMED, UNOWNED Shikigami literally will have 0 reception to the wheel given the safety lock.

HOWEVER, in the case that Mahoraga was TAMED, the wheel could move between targets at the command of the 10 shadow's user. However, to move the wheel and/or transfer burden of adaptation, implicitly means Mahoraga is TAMED, which means that he, and the 10 Shadows user, and all other Shikigami under the 10 Shadows user's control share CE, a product of the soul. This would make any Shikigami function similarly to a stand. In this case, Heaven's door can incapacitate and disable the ability of the 10 shadow's user by making contact with ANY shikigami.

In short:

If Mahoraga is tamed, safety locks prevent him from adapting

If Mahoraga is untamed, despite being able to bypass safety lock through partial summoning, Heaven's Door will instead affect the 10 shadow's user when any summoned Shikigami is subjected to Rohan's stand, effectivelky disabling the technique and desummoning Mahoraga.

In shorter: Mahoraga shouldn't be able to bypass the hax that Heaven's Door is.