I am going to be a dissenting voice and say... no, this will not help you, provided your goal is to become a veterinarian. Yes, it will expose you some to the medical field and it will give you some great skills that will transfer into a veterinary job, but, overall, it won't make much difference in your applications to veterinary school.
If your goal is to become a veterinarian, then you really should focus on trying to get veterinary experience or even starting off with animal experience. I know that most places want you to be at least 16 years of age, however in briefly looking up information on CNA classes, you have to be at least 16 years of age to start those, maybe your school has some different offer, but that was what I found in looking things up about becoming a CNA.
If you really want to become a veterinarian, you will do more good in trying to get veterinary experience and animal experience than you would in going to become a CNA. I see that there will be no cost or at least minimal cost in becoming a CNA, which is a plus, if it were going to cost you money, I would say definitely not.
Being a CNA will get you some skills you can use in veterinary medicine... communication skills, responsibility, patience, etc, but, overall, it won't show to admissions committees that you have an interest in veterinary medicine. And they *may* even question if you started off interested in human medicine and ask why you switched to vet med. So just some things to keep in mind.
If you are at all interested in human medicine as well as veterinary medicine, then I think going the CNA route would be good to get you exposure to the human medical field, then you should seek out experiences to see what the veterinary medical field is like.