No.
As for the controller question, I think it's a matter of personal preference. I'd love to try both a hitbox and a stick but I cannot get either in my country so I'm stuck with my "trusty" ds3.
Its always a personal preference matter really. Mine just sort of shifts based on the kind of fighter I'm playing due to the sorts of inputs I'll want to make. Things like plink dashing, piano-ing and wave dashing are generally tools that require stick to run properly to get your footsie and combo game on par in some games. Others these things might not even exist so its just a sort of tossup for me based on game mechanics what I'll go for.
Hit boxes are awesome by the way. The ability to roll your fingers for tatsu motions and speed input directions is incredibly awesome. Closest way to experience what it feels like is to find a fighter that lets you run keyboard for inputs. Its like typing only more fun to use a hitbox. If I get extra income I definitely want one someday. Stick will have a feeling out period anywhere from a week to a month if you never used one. Buttons are a non factor, but most people struggle to readjust to doing shoryukens on stick. Best thing is to get someone with QCF and Half circle motions and to go into training and try to do fifty of each move. Once you can do that consistently your good. Most don't really take long, but I've read of some folks just struggling like crazy to adjust for like a month. SRK motions aren't bad if you tap forward then slam it down and QCF. It reads it as SRK instead of Fireball if you tap forward first since there is general input leniency these days that gives you a window to hit your move even if you over rated and brought the stick all the way forward again on a SRK attempt done the way I said.
Course injustice is all super easy inputs so I doubt ANYONE would struggle to adjust to it on stick. A week would likely be pushing it. Advantages to stick are pretty good on games with tricks like plink dash, backwards wave dash, piano inputs on combos, and stuff like that. Pluse half circles are a cakewalk on stick. Tatsu is super quick and smooth to do on them.
All title related advantage talk aside though Sticks vs Pads is just a matter of comfort. If you can't consistently hit an input on one and thats with practice try switching to the other. It helped me get the speed I needed to hit a few tight links in some games I was missing. However, if you do well on pad then I don't think stick will make you any better. Its all about comfort and if you are already in your comfort zone on a pad it won't be much different for you on a stick once you achieve that same comfort zone.
You play best on whatever tool is most comfortable to you. I needed better dashes and faster tatsu's so Stick worked for me and It just sort of became familiar to me so I use it for all my other fighters too so long as they don't require me to hold a button to block.