Yes your action would depend on your emotion. You are reacting to how you think and feel at the moment in order to create the action that you are displaying. So yes I do believe that you would need both in order to achieve the other and get a proper response.
I believe that all action depends on emotion, regardless of whether there is necessity or not. Because we are emotional beings, I don't believe we are capable of making a decision entirely without emotion. When you are in a situation where you need to take action, you tend to go over your options and pick the action you feel is best suited to the situation.
Yes, action depends on emotion, more than necessity, because people sometimes do far more than they only need to do. This can be a positive thing, when we are helping each other. It can also be a negative thing, when we make emotional decisions to hurt each other or to go to war.
When someone has an emotion then it follows that they could also be described as thinking an action is necessary for a reason. For instance someone is afraid so they run they think running is necessary to avoid a threat. Someone feels in love they propose because they think it is necessary in order to have a happy life.
Emotion v. Necessity. Indeed emotion v. Reason or emotion v. Logic are false dichotomies.
I believe action depends on both emotions and necessity. People perform different actions all day long and many of them are done for varying reasons. There is no reason to assume that action is just the result of emotion or that action is just the result of necessity. Action develops for a variety of reasons, not just one or two.