PIC18F4685

Can this be burned by the current Midibox Burner module?

Yes.

Is the operating voltage the same as the 4620?

Also, what program would effectively burn it?

http://www.ucapps.de/mbhp_burner.html

P18

*  12.5V for a PIC18F or PIC16F…A device

* 13.1V for a PIC16F… device