is this an option?

No but there is a workaround.

HIDE ON LISTS
You can hide profiles on lists with "SQL Custom Where" here a docs: https://www.easy-profile.com/docs/69-sql-custom-where-list-and-module.html

For example you can create a radio field called "Show public profile?" with alias "show_public_profile"with these options
1|No
2|Yes

and put in "SQL Custom Where" User List menu item or module this code:
show_public_profile = '2'

With this profile are not displayed on lists, but are visible by direct URL.

HIDE PROFILE
To hide profiles page you can do this with Joomla Template Override feature
- Create a file /templates/your-template-folder/html/com_jsn/profile/default.php
- put this code into file

<?php



defined('_JEXEC') or die;



if($this->data->show_public_profile!='2')

{

	JError::raiseWarning(403, JText::_('COM_JSN_NOTVIEWPROFILE'));

}

else

{

	include(JPATH_SITE.'/components/com_jsn/views/profile/tmpl/default.php');

}



?>

This override simply includes the original template if the value of the field "show_public_profile" is different from Yes, otherwise it returns an error message