Yes, except that leaves headless Fortune negative on every special, and would overall make her MUCH less versatile as a character.
Also, you could still do Fiber~Zoom (during the invincible startup of Fiber, when it hasn't been blocked yet), and have the Zoom touch them second, which would still make it safe.
I'm sorta surprised people don't think about that stuff. Guess y'all are really in love with those invincible reversals, eh.
 Fortune's HK Fiber does not have vulnerable areas out anywhere until it also has hit areas. It can ONLY trade or win, same with Cerebella's Titan Knuckle etc. That's reasonably good for a move even without invincibility!
You don't lose or win a trade...and winning the encounter puts them back out, in the air, far away from you, probably by the head. It is a pet peeve of mine that unless a move leads to a full combo it doesn't matter that it does damage or moves the opponent or costs them meter or whatever. That's a complete scrub mindset.
Headless Fortune has SO MUCH crazy pressure and full stage shenanigans, not to mention a low-profile slide, that her having to block up close bothers me zero.
Once again, I am not here to argue. Especially with people who don't look at the entire picture, I guess.