It should be possible as long as the Ticket you are calling is within the same flow.
The local action would be configured for "look for new assignments to perform"-- the same as with a regular flow action.
Calling a Ticket that is attached to an End Shape within the same flow is a way to remove an unwanted assignment from a case without causing anything else to happen.
But why do you want to use a Local Action to attach a file when you can add one or more at any time using the Attachment Section's "Add" button within each Harness?
Attaching a file requires a commit which in a flow would be issued by FinishAssignment.
If I recall there is a PDN article about being careful when using the Attach Content shape at the beginning of a flow and expecting to know the pzInsKey of it's Link-Attachment right away - something like that.