This functionality is currently not in the Employee Portal and thus is not standard.  I have also checked the current 15.4 developments and find the same, the Attachments load is still handled the way it always has been.

I can inquire whether they are going to add this to a future release but for the moment this would be a change request to add it sooner if they are planning a future implementation.

I have confirmation there are no active plans to add drag & drop functionality to the Alliance line of products at this time.