The quick and easy answer to this is no. Just like Facebook, Twitter and Instagram, just because you delete the app off your iPhone or Android, it does not mean your account has been deleted. That being said, you will need to remember your username and password to log back in when you download the app again. Most people have their password and login saved on their phone therefore they do not remember it when they have to type it in again.
Also remember that your account is assigned to a telephone number and an email address. If you want to create a new Snapchat account you will have to use a different email address or a different telephone number. It is very important to use an email address in which you have access. If you use a fake email address you will not be able to use the forgot password option if you do happen to log out in the future.
To answer your question, no, if you delete the Snapchat app, it does not delete your account.