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)
Keep in mind, The Query filter always applies. If you use the above filter for set your Custom List to only show Test Cases that do have attachments (for instance) then any further filtering within the app (using the app's built-in filter option) will be in-addition to the Query, so that will allow you to further filter within Test Cases that already have attachments. In the same way it will be if you used that Query to exclude Test Cases that have attachments.
You can include more than a single instance of Custom List in your dashboard, so what you can do is include a permanent instance that only filters with attachments while another the filters without or does not filter at all. This way, you have both representations on your screen at all times. Alternatively, you can choose to only create this Query filtered instance only upon demand if you need it on occasion.