Did the Byzantines manage to achieve the desired result after the conclusion of the Ferraro-Florentine Union?

The Pope promised to help the Byzantines in the war with the Turks in exchange for union with Rome. Byzantium was threatened with conquest by the Turks, and the Byzantine emperors agreed to conclude a union. Union was concluded at a council in 1438-3149 in Italy, first in Ferrara, then in Florence.
The union had many opponents. The signing of the union in Russia did not find support. Metropolitan Mark of Ephesus, a popular personality in church activities, did not sign the document. The common people also opposed the union.
Union did not save Byzantium. The support promised by the Pope came only 2 weeks after the capture of Constantinople. The signing of the union did not achieve the desired result.