No, deactivating and installing Email Users will not have any affect on your existing users. The only possible exception would be they might lose their Email Users notification and bulk email settings but those are easy to fix from the Email Users -> User Settings page.
FWIW - the text you modified is the Default Notification Body and changing the text in the plugin source code will not have any affect on what is sent to the users UNLESS you changed it before you activated the plugin. That paragraph is used as the default value for the notification text and is stored in the WordPress database.
You can change the value of the notification text by going to the Email Users Settings Page.
To fix your problem ...
Do you have FTP access to your site? If so, I would reupload the one file you changed to replace the one on your site without de-activating the plugin.
If you don't have FTP access then your only choice is to remove and reinstall the plugin.