Answer
Yes, this is generally achievable with a Custom Event, though it takes a bit of tracing to set up correctly: use the Debug tool to identify exactly which underlying condition/event actually triggers the specific error-message dialog you want to catch, then build a Custom Event tied to that same underlying triggering condition, with an Event Action configured to push the notification into a Stream. The general concept is the same whether the error occurs during an interactive transaction or within a background job — trace how the specific message gets raised first, then attach a custom event to that same trigger point, rather than trying to hook the error-message dialog itself directly.