Only in certain situations. The Hogyoku can only realise the desires of beings who have the innate potential to do so themselves. It's not outright reality warping like Shunsui's Bankai nor is it probability manipulation like Gourmet Luck from Toriko. Moreover, Aizen was overpowered and eventually beaten by Dangai Ichigo alone, so I doubt he can solo the entire Gotei 13. Yamamoto can debatably beat Aizen by himself and Shunsui's Bankai is incredibly hax as well. Anyway, I don't want to derail the thread into a Aizen vs Gotei 13 debate so I'd prefer it if we just stayed on topic.
In your opinion, which team wins?
This is actually false, anyone who watched/read aizen vs ichigo can tell you ichigos final getsugatensho (which used all of his power so much so he lost his power after) did not kill aizen. It didnt even defeat him. He was defeated by a kido seal hidden within a kido by urahara.