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