You can indeed bring your Yith with you after you transmog, however, it's not especially game breaking:
Yith wrote:Your Yithian hands you a piece of metallic paper detailing your fight. It points out a couple things you hadn't thought of, and you find yourself thinking more about this combat. You gain 3 XP.
Old Friend wrote:In between fights you catch up with your friend, who seems to be full of "do you remember the time we ..." stories. Rehashing the best of your past is kind of nice, you think. You gain 5 XP.
Sculptor wrote:Captain Cannon Fodder makes a little sculpture of a uniformed civil servant. A police officer or fireman or something. You both pause to appreciate its beauty before it melts. You gain 1 XP.
Spider wrote:The spider does a shuffling little dance that partially reenacts some of the best moves from the recent fight. In a weird way this allows you to better understand how you won. You gain 3 XP.
I also tested the Yithian's damage:
Your Yithian points the strange weapon at your opponent and gives it a powerful blast. It does 12 + 12 damage.
That's probably a little more extreme, especially when the Gnoph-Keh and Hound of Tindalos were doing 4+4 or 5+5 (which is still a fair amount of pain at level 1).