Is paying the annual Zakat on the first of Dhu al-Qi'dah on all wealth, including the salary of that same month, and giving it to a former mosque imam to distribute it among needy relatives and neighbors, Islamically sound?

Zakat (definition) is not obligatory on cash until a year has passed over it and it reaches the nisab (definition) (minimum taxable amount). It is permissible to pay Zakat in advance. There is no harm in entrusting a reliable person who is knowledgeable about the legitimate channels for Zakat distribution, as mentioned in the verse: "Indeed, [prescribed] charitable donations are only to be given to the poor and the needy, and to those who work on [collecting] them, and to those whose hearts are to be reconciled, and to free captives and debtors, and for the cause of God, and to the stranded traveler; a duty imposed by God. And God is All-Knowing, All-Wise."