I'm not sure what you are asking. We all have emotions. But, if you are emotionally very sensitive, it might be difficult to learn how to control your emotional reaction to incidents. As an emergency worker, you will be exposed to many intensely emotional incidents. Most of us learn how to maintain a professional demeaner in the midst of it. Most of us are able to leave the calls at work in most cases. I guess the deciding factor is not 'do you feel the emotions' but what do those emotions do to you and are you able to deal with them in a way that will still allow you to do your job.
Like all jobs, the people in EMS run the full spectrum of different personalities. Some handle certain aspects of the job better than others. I know one medic who is pretty 'touchy-feely' and likes to visit his pts in the hospital after they are admitted. Personally I find that a bit extreme for me, but he's been doing this in a civic department for over 20 years and it seems to work for him.
Personally, if a job was going to send me into fits of depression, weeping, kicking the dog, or other uncontrollable displays of emotion, I'd find other work. There are calls that get to me, and in the years I've been doing this, I have probably felt every emotion possible, Sadness/Grief, Anger, Joy, Panic, Relief, Stress, Tension, Fear, and probably a few I missed. There have been calls that stuck with me and experiences that will always be raw spots in my psyche. But, so far, the positive outweighs the negative for me.
I hope this helps.