Would this be a Church/State conflict?

FTR, I think that it would indeed be a violation. Government is to remain neutral, neither promoting nor prohibiting free exercise. If this were a private business and privately funded, one could promote either Christianity or atheism, both or neither. However, when the government provides funding, one relinquishes some of their autonomy. Christians would not want their taxes promoting atheism, nor would atheists wish to fund Christian proselytization.

This is one of many reasons that I believe President Bush's constant pushing of "Faith-Based Initiatives" is a bad (and unconstitutional) idea. Once the government is paying the bill, it calls the shots.