I created a ticket about this Presonus Sphere but rather than answer the question, it redirected me to making a feature request here, so I'm assuming "No, this feature doesnot exist":
"Is there a way to set a project playback global shuffle/swing. I'm aware of using th "select all midi and set quantize" method but a) it's not real-time meaning you choose a random swing amount and hit apply and you repeat this until you hit the sweet spot.. I'd like to tweak it and hear the changes take affect and "interactively" find the sweetspot. Second, it applies to the notes already entered. If you add notes, you have to remember to re-do that swing and if the swing changes for some reason during those millions of times you hit quantize, the whole song is ruined.. The way I work with swing, is start with a groove/beat/bassline, set the swing/shuffle and build the song on that groove-feel.. Maybe some people like setting the shuffle/swing after the song is done, but I can't imagine it working for me.
So, some kind of project global swing that would be more tactile and time-based (?) Perhaps there already is something like that in S1 but I just haven't found it :)"
Now, I'm sure this question has been asked time and time again, but I think we (the users) are entitled to post this until it gets addressed.