Very nice idea. The only issue I see is that you have to give access to everyone to the uploaded PDF, which in some jurisdictions is a copyright infringement. But that is just a technicality, with better PDF plugin or a way to assign AI a google account, that would not be needed
I mean that, according to the article, with the way the plugin works right now in order to pass it to ChatGPT you have to make the file accessible to the whole world. From the article it seems that Chat is unable to connect to google cloud with an account that you could limit the access to, the PDF has to be viewable without login