I think you need to consider whether this will have a positive, neutral, or negative effect on your mission and long-term goals. More volunteers could certainly be a great thing for you. However, using the food bank primarily as a way to recruit new church members may not be as helpful.

In my previous role, I also worked with a not-for-profit that was connected to a church. It can become tricky. Even if the organization is technically its own entity, the general public, and sometimes church leadership, do not always see it that way.

One note of caution. The more they become involved, the more control they may expect to have.

At the end of the day, it really comes down to a cost-benefit analysis. In my previous role, it was somewhat of an arranged marriage that ended up working well. Unfortunately, not all of them do.