Imagine a darius, a morde, an aatrox with Yuumi. You have these juggernauts that don't have tools to engage then you equip them with an invulnerable character stacked with engage tools that boost their damage. I think we might see a meta change, at least at the pro level, revolving around Yuumi... or she'll be permabanned.
I think you are greatly overestimating Yuumi's "engage", especially when said engage boost is a light MS boost, a slow IF her Q has been traveling for a while, and a Root if 3 of her ult waves hit a target.
If you think that will make Juggernauts broken and have the meta shift around them, may I remind you Lulu or Zilean exist, both of whom provide far more utility that a Juggernaut cares about.
I should point out that Yuumi is not invulnerable. She is simply UNTARGETABLE. These have entirely different connotations.
Let's take 
Vladimir as an example. Vlad is untargetable when he uses his blood pool ability. However, he can still take damage, and any lock-ons will remain locked on until the ability, effect, or channel is completed or interrupted. Yuumi will still be entirely vulnerable to AoE attacks, and things like Cait's ultimate or Fidd's drain. The hard counter here, I think, will be champs who excel at doing large amounts of AoE damage, like Ahri, Anivia, or even Singed.
I don't think so to say the least and she doesn't give damage boost like Sona Q.
Since Yuumi seems like a fine champion, the only question to keep in mind is how her scaling will be and her cooldown are.
She's not even fully untargetable. She's only untargetable while Attached. And even then she loses the ability to basic attack, as well as to use her own positioning for zoning - which are powerful engage tools that high-level supports utterly depend on. (Good Yuumis will probably need to master the art of unattaching into high-damage attacks to bodyblock them, I'm guessing.)
I can't think of a lot of pro teams who would play a 4v5 in exchange for better juggernaut stats right now. I see Yuumi as probably boosting the performance of high-damage ADC's who lack survivability - 
or particularly 
, broken and top-tier as she already is - more so than juggernauts. I'm not saying you won't see pros possibly picking 
to synergize with her, but I'd be surprised if she fully breaks the meta; however, I've been wrong before. A lot will probably depend on how strong her ult is.
too bad I'm never letting her get picked then huh
I think we might see a meta change, at least at the pro level, revolving around Yuumi... or she'll be permabanned.
That's basically league in a nutshell. Anytime a champion is meta-defining, they just get banned out.
