I main Illaoi with 35k mastery points. It's not alot, but I do know her ends and out. I don't think adding the slow would be the best idea. Adding the slow on her kit is going to give her appeal to newer players, but to those who can play her well, it's going to become super oppressive to whoever Illaoi is laning against. Wasn't one of her INTENDED weaknesses was for her to have almost NO CC nonewhatsoever? This still doesn't fix none of her fundamental problems, nor her W/Auto attack bugs, her E unreliability, none of that.
If you're good at her, Illaoi is pretty decent right now as she is on live.
If anything, the Q slow needs to be reverted, and her E needs to be more reliable on how she actually pulls the target. Or possibly give her a slightly longer vessel time. Also, once people get the hand of her, Riot is going to notice, and nerf her into the ground.
Please, the slow isn't even needed and just overbooks her kit and removes her weaknesses. Fixing the bugs (if possible) or moving the slow to the E (longer E slow once the target becomes a vessel).