Try to play the file in the DropBox app. It'll come up as a text file of code.
Tap the arrow icon on the lower right corner. You should see options for apps to open the file in.
From the options you can "Play Audio File" or "Cancel". Either way, the file will be there in the iFile documents folder and you can take it from there.
PS- I just looked at FullDrop, but it's listed as not compatible with iOS 5.
I use "iFiles" from the App Store for most of my DropBoxing. It does more with DB than the official DB app does.