You can set access to your Google Site to control who can work on the unpublished version of the site and who can view the published version.  Each person that you give access to the site can be set as an editor or a published viewer.

To set site access,  click on the Share button near the top-right corner of the screen.

Click on the Cog in the top-right corner of the Share screen to choose whether site editors can publish, change permissions and add new people to the site.

You can also choose how people can view the current draft or published copy of your site:

If you have shared the site with everyone in the organisation, click on the Settings button in the Links dialog box to chosoe whether people in the organisation can search for the site in Google Drive.