Yearly collection and distribution of gifts to our church's missionaries

There is an on going debate between the treasurers and the mission committee of our church that we really need a sound answer for.

The mission committee takes up an offering every year to send monetary gifts to all of our missionaries. It is sent to their mission board, not to them directly. No one,except the church mission committee designates who gets the money, just that it goes to the Christmas in July fund, which supplements the budgeted Mission's Christmas Gift line item.

If individuals put the money (or a check made out to the church) in special envelopes and do not designate an individual missionary as recipient, is the gift tax deductible?