It's not possible without an add-in.
You could write a query for the report generator with an ECO number prompt that gets the file list. Then copy and paste it to that variable field on the ECO data card. Someone has to stay on top of this when files get added or removed.
Via the API you could do a lot more such as automatically updating the "Affected files" field on each transition of the EC. There are certainly individuals here that do this kind of work and could probably turn around add-in like this very quickly. I'm sure the cost to do this manually for each EC would quickly eclipse the cost of the add-in.