I see, diode keep voltage level equal to forward voltage....
Does schematic you posted work well with Due?
Means is voltage treshold low enough?
I don't know.
You would need to look at the datasheet for the SAM3 micro on the DUE, as well as the ATMEGA16U2 chip (because the reset line runs there as well - see attached schematic) for the reset pins specs. I believe that in addition to the on-board 100k pull-up on the DUE pcb, the Sam3X has an internal 15k pull-up on this line as well. I do not know the internal setup, or requirements, for the ATMEGA chip.
It would be pretty useful for my app,however I can('t) see pullup in the circuit you posted.
Question is also, is that pull up resistor essential? If yes, desired value would be 10k?
On the DUE side, you would not need to add any additional pull-ups, because they already exist on the DUE's pcb.
In any case, ~10k-15k is a typical pull-up value in this role.
As far as I can tell, you won't hurt anything on the DUE; and it will either work, or not work...