Hi @nathanpenrod,
I am sorry to disappoint you but the viewer does not support selectable or searchable text within the embedded PDF document. This is something that we are looking at adding to the plugin in a future update; I will add your comments to our feature request list to record your interest in this improvement to the plugin.
I do want to mention that while the contents of the document are not searchable when viewed by a user, the contents are available to search engines for indexing and SEO purposes. The documents can also be searched for on your site just like any other media items, page, or post using the WP search functionality using the media title, description, and other meta data.
If you have any other questions, please feel free to send an email to contact@wp-pdf.com as we may not see messages posted here to respond in a timely fashion.