No. Once you have been placed in the ESA work-related activity group or the support group, which would have been determined by your successful appeal, you no longer have to provide sick notes.
Nothing on this board constitutes legal advice - always consult a professional about specific problems
Just a note, I received a letter requesting a sick note yesterday, despite being in the WRA group. It was, apparently, a computer generated letter, so the computers are now in charge methinks!