Unfortunately, there isn't any public API to AirDrop. Hence, Path Finder doesn't support it (nor it ever did). We're working on implementing our custom solution for AirDrop functionality, but we can't provide any time frames, sorry.
There is an easy work-around using Keyboard Maestro (and surely any other scripting or similar program). ⌥⌘f opens the current selected files in Finder. ⌥⌘r (in Finder) opens AirDrop (but doesn't populate it). The Keyboard Maestro macro (image attached) will open an AirDrop window with the currently-selected-in-Path-Finder files. The image used for "Found Image" is a screen-snap of the Finder "AirDrop" Toolbar icon.
It's been over a year since this post was started. I have to continously open finder so that I can use AirDrop, which I use all the time. I don't need a work around as Finder does it just fine. One of these days, it's going to be easy enough just to keep using Finder instead of Path Finder. I would rather that not happen. I do like Path Finder, but its a pain to keep having to jump back and forh to Finder when I could just keep using it.