As far as I know, the game doesn't tell you that it isn't viewable in battle, could you show me where that's stated?

Also, it's not the responsibility of the player/consumer to find this out on their own- that's just terrible design, it's up to the designer to make that apparent as possible as that is their job as designers, seeing as every other outfit is 'generally' shown in battle, without the game giving you some sort of signal "Hey this isn't shown in battle", then no, the most common conclusion is that it is shown, the game/designers just did a terrible job at relaying information.
That is not the fault of the player.