Sayu is a kind, considerate, beautiful human being so she probably would.... or maybe not
One of the great things about her is even though she's doing a great job as a leader, putting the group first and promoting it and the other members every time she had a chance, she's also very self conscious as an Idol and tries her best not to get buried underneath all her new duties and still manages to stand out as a member of the group herself.
Remember her birthday T-shirt design last year ?
Kekkyoku Michishige, the second part of Michishige Hitotsuji series :
"Even though I got swept away by the younger girls, it's Michishige for me after all" I fully plan to oblige her this year :> ... not in small part because you all heretics already kicked off the future queen. Appropriately enough, everyone here beside Sayu are leftovers from that accursed group too so lol, talk about an easy choice.