In short, no. Here are part of the terms as of Feb 2017
- you agree not to access Content or any reason other than your personal, non-commercial use solely as intended through and permitted by the normal functionality of the Service, and solely for Streaming.
- You can read these terms yourself, they are nice and short! Pop over to YouTube and click the little Terms link at the very bottom of the page.
- So, as a church service is (usually) a public service and definitely not a personal activity then the YouTube license does not allow playing of videos in church services.
YouTube terms were updated in Summer 2019, the section on Permissions now says:
You are not allowed to:
9. use the Service to view or listen to Content other than for personal, non-commercial use (for example, you may not publicly screen videos or stream music from the Service);
Here’s a screenshot of the section:
So, YouTube still only allow playing of videos for your own personal use.