If what you want is a custom web app with some visualizations implemented by Tableau Server, yet to have those visualizations embedded and controlled by your custom application, then Tableau has a lot of options for you.
See the sections on "Embedding" visualizations in the Tableau help pages. You may also want to use the Javascript API (start with the excellent 5 minute tutorial). That API allows you to control interaction between your application and the embedded visualization to make the integration more seamless, and customized to your needs.
To avoid forcing your users to authenticate with Tableau Server, read about Tableau's solution to Single Sign On and/or read about Trusted Authentication (which lets your application vouch for a user's identity if you have a core based license).
All these features are described in the Desktop, Server or Developer guides on Tableau's help pages. I recommend embedding using the object HTML tag instead of the iframe tag. Both work and both are documented, but the object tag gives you more control, works well with the JavaScript API and avoids some of the legacy HTML issues surrounding iframes.
If instead, as you stated, your only goal is to produce Excel or PDF output, Tableau can do that - one easy way is to append .pdf or .csv to URLs. Again read the documentation on embedding. But if that is the only goal, especially for CSV, Tableau is an expensive way to simply generate a CSV file. I'd give some thought to your requirements. There are reporting packages that are focused on hard copy tabular reports (sometimes called report factories) - that's not Tableau's primary focus.
One approach that can be helpful, use a modest investment in Tableau Desktop to quickly prototype your visualizations and reports. Verify you are producing the right outputs and that you have the right data to create them. Then you can decide whether Tableau is the best way to meet your requirements in a production environment. Even if you use a different approach in production, it can be very helpful for speeding that initial investigation.
