Adding a custom column to the entries table

How do I automatically add a pseudo-field (like payment_status) to a form and have that field display on the entries list table?

Background:

I'm working on a connector to allow Gravity Forms to talk to a contact centre system. I want to record whether the remote connection succeeded in a send_status pseudo-field and show that on the entries table so connection problems can be clearly seen. I think GF already uses the payment_status pseudo-field to do something similar?

I think I can use export_fields to add in the field, but I can't see how to get that field on to the entries list table. Actually, I don't think I can use export_fields to do this. Darn.