Yes. The DC metro area probably has the highest LEO density of any area in the world. Noticing a plain clothed person carrying is not unusual and over the years I've noticed quite a few visitors to the church "carrying". The carrying part isn't the problem. What would bring their presence into question would be their demeanor.Blaster almost certainly has more experience carrying in a plainclothes environment than anyone else I know. I certainly respect his view and don't disagree with where he lands on it.
That said, I would offer this thought. I've carried off-duty, everywhere I've gone for 22 years. I've always operated under the feeling that there were very likely other armed people about that I simply didn't know about. In the event of something like an active shooter, if I move to contact than every other armed person there is 1) a possible threat, 2) viewing me the same way. When uniformed police or security arrive, failing to follow their orders may get me shot so I'd better pay attention to them.
I guess I just don't see the difference that makes a church different from any other place that may be employing non-uniformed, armed security or occupied by lawful carriers. If I go to the mall, I'm not stopping at the security office to check in. I don't alert the Amtrak police or Transit cops when I ride the train. Maybe that's a failing on my part.