The stick doesn't help it, only makes it harder because you will quickly realize how slow the animation is responding to your inputs, instead of being precise you will also have to start timing when to execute the dagger input when after you hold up which in consequence, makes the iaD precision very inconsistent, because of it, you won't hit grounder characters when you need to because Skarlet iaD to connect it needs to be executed flawlessly on very 1st frame the character gets airbone, or on the second frame which will catch them in the top of their head. Even if you jump backwards of towards, the character should've be able to jump at the tap of the button not by holding up for 3 frames to jump, its stupid, its silly, its a bug, specially when the game recognizes that you pressed up but the game system won't respond accordingly, is a Input Bug.
On the D-pad is much easier because the way the D inputs are layered you can easely access the other directions after holding up for very about 2 game-ticks. This is why most of us Skarlet players could most of the time get the first iaD but couldn't fire a barrage of it, when i bought my stick it was not only to improve my Street Fighter Execution and board forwards in the horizon of dificulty and extreme level of execution where monsters like Sakonoko and Desk stands, but to be able to experience the same level of deph in Tekken and of course improve Skarlet execution to a level that it wasn't possible to achiveve in the D-pad.
Unfortunately, Daggers are a major part of her playstyle and play without it is like handicaping yourself, specially those iaD (low daggers) which are the ones she needs the most to OTG any character in the game and block their mind for thinking a better solution to escape inumerous offenses and setups that comes from that single OTG.
As far as i know, Input Bug affected both Down and Up not only down has some ppl are sure of it, and not only up as Dizzy said once, it affects both, many times i got grounded daggers when i tried to perform iaDs because the precision jump was too good that by tapping the character wouldn't even jump.