If it came down to it, if you HAD to, if there was no other choice; in a battle to the death.
Would you allow your captain to kill you? Does your loyalty stretch so far to lie down your own life at his own hands. Is it MORE than loyalty?
Or would you kill the man that you've sworn allegiance to past the empire itself, to survive; to go on with the fight?
Your question, or rather, questions, are charged, and complicated to answer.
Were I not in charge of an important mission, I would not mind dying by my Captain's hand. It would be... preferable to other types of death, although I dare not imagine what could have led to such situation. Your guess is correct, but that means that it is also loyalty.
However, that is not the case. I have accepted a very significant role and, at this point in time, one that I believe impossible to delegate. Kirk would undoubtedly deviate from the path of the revolution and steer the movement for his own gain shortly after I was no longer there to oversee his actions.
If there truly was no other choice, I would kill James Kirk for the good of the people subjugated by the Empire.
I would also regret this every day of my life and, if the revolution succeeded, I would...