The Theme provides template files, functions and front end resources; CSS and Javascript. And it saves some theme options in your database.
But thats it, it doesn’t influence any core functions and it does not interfere with any of your content ( posts, media etc ). So updating a theme won’t impact that, it may simply change how the front end is displayed.
For peace of mind though; have you spoken to your hosting provider ? Ask them to make a site backup or if they have a Staging server option, which will give you a clone of the site to make changes to without affecting the live site.