I have an additional information:
I just found out that if you use Mail.app, it is possible to drag and drop an attached .pdf. The drag and drop movement is accepted and the file is processed by the filemaker scripts I have written.
But dragging a message in its entirety (.eml) does still not work. It is the same as with Outlook for Mac 2011, the drag and drop movement is not accepted. If you first drag the email to the desktop, and then to the drop down zone it works...
The drag to your desktop will trigger some kind of interaction between the mail app and the OS and the creators of the Mail app probably wrote specific code to support it to produce the file on the desktop. It would seem that this same type of interaction directly between the mail app and FileMaker, on the other hand, is not supported.