Deleting the "Page title" module in an existing site that needs some module-removal (Will damage SEO?)
Page Title stores its titles in a DB table, which will be deleted (along with all its data) if you uninstall the module. It uses an HTML preprocess hook to load that data from the DB on a page-by-page basis, and replaces whatever would normally be the title for that page right at the last minute.

So...


  I wonder if deleting it will destroy the page titles that have already been added to the site's nodes


Is entirely accurate. If you remove the module, you'll also remove the page titles that were added using it, and Drupal will use whatever default title was applicable for the entity before you installed it in the first place (e.g. for nodes that'll be whatever is in the title property).