Transmogrification Faction items

[lachukss]

Hello.
Wanted to know if tis works or dosen't <3
lets say, i buy via store Cloak >Drape of the Refreshing Winds< horde faction item.. As alliance.. Will it not change the faction automatically?
I can't equip it, but can i mog it so i keep the yellow, red look? As alliance?
Alliance has it in black. blue..
Transmog's will not change look, if i do faction change?

Wotlk realm.

Thanks for Help.