Yes, this can be done. Do you have the Acrobat SDK? You can access the documentation here:
http://help.adobe.com/livedocs/acrobat_sdk/11/Acrobat11_HTMLHelp/wwhelp/wwhimpl/js/html/wwhelp.htm?&accessible=true
To find out if the document you need is already open, you need to first use the AcroExch.App.GetNumAVDocs function, and then iterate over all open documents using AcroExch.App.GetAVDoc
Now you can - using AcroExch.AVDoc.GetPDDoc and PDDoc.GetFileName - find out what the filename for each document is. At this point you also have the PDDoc, which you need to fill in the form fields.
Karl Heinz Kremer
PDF Acrobatics Without a Net
PDF Software Development, Training and More...
http://www.khkonsulting.com