I don't know of a way to make it happen automatically, but if you were to have FileZilla start with Windows, you could use an AutoHotKey script to achieve this (obviously you'd also have to have the script start with Windows).
I don't know how to post something that's compiled (in case you don't already have AutoHotKey), but here's the source of a script that works on my machine...
SetTimer, s_CheckWindow, 5000
IfWinExist, FileZilla ahk_class wxWindowClassNR
WinWaitActive, FileZilla ahk_class wxWindowClassNR, , 10
The script checks once every 5 seconds to see if FileZilla is running and if so, activates the window and sends CTRL+P to it (the shortcut for "process queue"). Once it sends the CTRL+P shortcut, it exits the script.