Are search engine bots able to index precompiled Web applications?

I don’t know about other server-side technologies, but ASP.NET compiler provides the option of generating a complete application as a compiled DLL.

As the content is all compiled and is in binary, how will search bots be able to crawl through the content and index words, meta tags, etc?

Yes, it can. The server side web application generates HTML for the user to view on their browser. Google bots simply look at this generated HTML like a user does.