Yes, this is the logical extreme. Showing the absurdity of the extreme demonstrates that all points along the continuum are subject to question. Nothing about our government system was intended to be despotic. Conditioning a welfare recipient's benefits on purchases that are non-religious in nature would excessively entangle church and state and would prohibit the free exercise of religion. The money is the object of the program.
Education is the object of the public school program.
The recipient of the money can make purchases based on the dictates of his own conscience, and if he values supporting his local church over food, shelter, medicine, etc., it is his right to do so. Those are legal principles that would have direct bearing on your effort to make a case concerning the fact that someone who is on welfare might put some money on the collection plate in church, or should happen to buy something at a church bookstore, etc.