Question: Would you happen to know statistics on the average number of people who actually attend church after being invited? For example, if we give out 100 flyers or mail 100 letters, what can we expect to be the outcome?

I cannot answer your excellent question with any accuracy. Here are two related answers:

The Southern Baptist float a statistic from several years ago that says people attend after an average of 13 invitations. I cannot verify the validity of that number. I cannot even tell you how they arrived at that figure.
The people who do direct mailing say a 1-4% response is acceptable. Some of those responses include, "take me off your mailing list."
My response is not adequate, but represents the total of my knowledge on the subject. I am pleased you are trying to identify results in order to determine your effort and the use of your resources.