No, publishing a course/policy via MetaEngage will only trigger MetaEngage prompts for those users who have Client installed on their device.
Users, who do not have the Client installed on their device, will not get the prompt for the course/policy; and neither will they get an email notification instead.
It is important to ensure that all those users, who you would like to target via MetaEngage, are on a device that has the Client already installed.