No, that plugin won't "deactivate" email in any other plugin. All that Easy WP SMTP does (and similar plugins) is hook into the Wordpress mailer and set it to send through a SMTP account rather than the PHP sendmail default server mail.
So, Easy WP SMTP will send ALL Wordpress generated emails through SMTP once you get it set up correctly. That includes any other plugins that use the WordPress mail function, so they will all still function correctly. If the other plugin you mentioned has its own direct SMTP connection (you would have to set it up via some settings), then it won't be affected at all. Or, if that other plugin is doing it the wrong way and calling the PHP sendmail function directly instead of going the the wp_mail funciton, then it will continue to do so since it will be bypassing the wp_mail function.
Best thing to do is to install it and test it out to make sure it works with everything on your site. It's a very simple plugin that only does one thing, so the chances of it conflicting with or breaking other plugins is very small.