I have used a pdf file for this scenario.
1) Open your pdf from its original location.
2) Move the file to the destination folder on Dropbox by dragging and selecting "Move Here".
4) Close the pdf.
5) Repeat Step (2).
6) Select "Move and Replace" from the second dialog.
7) Select Cancel for the first dialog.
--> File disappeared without any trace for its existence!
And not in the Recycle Bin.
It is worth mentioning that I have tried the same procedure using non-Dropbox folder; however, the file was maintained in the destination folder.
Dropbox 2.0.22 (Identifying Dropbox Windows 7 client version)
Microsoft Windows 7 Professional SP1 64-bit