No, only files in the plugin folder in wp-content/plugins/ will be updated. Each update only affects the directory of that specific plugin or theme.
So, if a plugin is updated all the files in that (plugin) folder will be overwritten and manual changes will be lost. If a theme is updated, all files in that (theme) directory will be overwritten.
If you manually edit/add files to your theme directory (like EM template files) they will be lost when your theme gets an update. If you are using a theme that receives external updates, it’s best to start using a child theme.
https://www.hostinger.com/tutorials/how-to-create-wordpress-child-theme
If a plugin is updated, files in your theme folder will remain unchanged. Just like your theme is untouched if a plugin updates.
When EM calls the function locate_template() it will first look in the correct folder in your theme to see if it is there (its presence is interpreted as being modified). And if present, it will load the file in your theme dir. If not, it will default to the template file in events-manager/templates.
So, if you copy all template files (also the not-modified ones) to your theme, you will always be left using that version. Updates within EM will be ignored. That is why you should only copy the files you actually edit and modify.