No it shouldn't 1 because a subdomain is treated as another domain with its own root folder.
in most cases you will have something like:
www/ - this is where your site's files and folders are and most people will call it the root directory of the site.
Your subdomain will look like this:
www/folder/ - which the folder is now where the subdomain lives and is treated as the root folder of the subdomain.
so if for any reason you want to remove the application it will not interfere with the main domain. All you have to do is remove the subdomain which will either remove the subdomain folder or leave it so you can remove it manually and then remove the database you use to install the application or remove the tables from the database that was use if its being use by other applications and needs to be left there.
Most web application are not installing anything extra to the server or placing drivers or files on the parts of the server. They usually run from the folder which they are in and now and then they require access to a database just to create tables. Aside from that they are only checking to make sure that you have the right libraries and software to run and to help you create tables on a database.
So in short not it shouldn't but is good to know why.
