No, you cannot target Nicol Bolas using his own ability like that.
The relevant parts of the process go like this:
- You start activating Nicol Bolas the Arisen's ability.
- You choose the target for the ability. This has to be a card that is in a graveyard at this time.
- You pay the costs for the ability. In this case, that means removing 4 loyalty counters.
- After the ability is activated and before anyone gains priority, state-based actions are checked. At this time, Nicol Bolas dies because it has 0 loyalty counters.
As you can see, by the time Nicol Bolas finally goes to the graveyard it is far too late to target it with the ability.