I would say that this quote actually works on two levels.
The first level is, I feel, the more obvious one. It is meant to imply that, even at the moment of death, the character (Midshipman 1st Class Peter Preston) is ever the professional. His concern, even then, is for the ship and fulfilling his role. He is still looking to his captain for orders. The ever-professional element is further enhanced by the words of Scott just after:
He stayed at his post... when the trainees ran!
The second level to the quote is a little bit deeper, but follows the first quite logically, and I feel is the more important one, given the situation in that scene. I think that it is also meant to imply that Peter is also asking his captain for permission to leave his post (ie die).
I haven't found a source to back this theory up, so if anybody has any input on this, I'd be interested to hear.
Just to add to this theory, the phrase by Kirk is quite specific: "The word is given. Warp speed." Why the addition of warp speed? The captain wouldn't give the order 'warp speed' to a Midshipman. This part of the phrase is meant to emulate another phrase: 'God speed', usually used to express blessing to somebody going on a long and dangerous journey.