I did a quick searched and I did not find an easy way as you expected to customize the drop/drop operation to open file instead of import, but if you are interested in C++ code, I found Maya provided a callback way to help you hook into Maya’s drag-and-drop mechanism.
The classes MExternalDropCallback/MExternalDropData were introduced in Maya 2013, check here:
• MExternalDropCallback - This class will be used to register callbacks to gain access to Maya's drag-and-drop information when dropping external objects into Maya. You can replace or augment this drop behavior for external drag-and-drop operations.
• MExternalDropData - This class represents the data carried within a drag-and-drop operation when dragging from an external application. This class is used by MExternalDropCallback.
There is also an example at http://help.autodesk.com/view/MAYAUL/2018/ENU/?guid=__cpp_ref_external_drop_callback_2external_drop_... to demonstrate how this is supposed to use. I think that might be something you are interested, but requires more C++ skills.
John Wu
Developer Technical Services
Autodesk Developer Network