In the Custom List app there isn't a way to add the Attachments column to the view. In fact, there isn't a way to include the Attachments column to Rally's screen of Test Cases as well.
How can we filter out Test Cases that do or do-not have attachments?
Unfortunately, the Attachments column isn't available for Test Cases, Test Case Results or Custom List app.
However, what you can do with the Custom List app is edit the app Setting's and include a Query.
1. To filter only Test Cases that have attachments (at least one attachment) you can enter this query filter:
(Attachments.ObjectID != null)
2. To filter only Test Cases that do not have attachments you can enter this query filter:
(Attachments.ObjectID = null)