I think Stuart’s role was not so much to cooperate with Pickett in the attack as to exploit the confusion created by Pickett’s successful attack.
No success by Pickett and no resulting confusion would have meant Stuart attacking formed infantry with cavalry, which in this war never worked out very well.
Stewart's attack started long before Pickett started. Stewart was to get into the rear during the initial artillery fire mission and split the front. But he got tangled up well before noon on Pickett didn't start until after 2PM.
I've a book that was written just a few years back based on some newly found documents that dealt with the Gettysburg Battle. Much of the documents dealt with Stewart and his orders to attack the rear. He was supposed to get into position and when the Confederate barrage stopped he was to probe the Union lines in the rear and try for a break thru and Hopefully meet Pickett coming through from the other side. He never got close because of the ferocity of the infantry he met and then the hammer dropped on him by Custer's reckless charge.