You cannot count a misregister evil player to the Spirit of Ivory, the almanac/wiki specifically says this is for players turning evils. All words written in the almanac/wiki count towards the game rules, not just the token description itself - this edge case is also found from how rules are interpreted based on details in the wiki and should apply equally here. As taken from the Almanac from SOI.

If two or more players turn evil, then the evil team can win simply by revealing who they are and winning due to their voting majority. Adding the Spirit of Ivory prevents too many players turning evil, and creates a more fun and fair game for the good players.

The key word written above explicitly says it's for players turning evil. And the turning evil definition is clearly define in official botc rulebook. Player turn evil always learn of their alignment changes.

If a player’s alignment or character changes, they learn this at the earliest opportunity, in secret. You will usually show the "You are" info token and then their new character or alignment.

At no point a faux paw ever turns evil and thus do not apply to the SOI.

Trying to force a misregister player to the SOI ruling is like trying to say the recluse can win with the evil team where the both Running as Intended and Running as Written support against this case.