You connect to SQL server using one of several methods: Named pipes, shared memory, TCP/IP. Once you connect, you communicate with the server using the application-defined protocol called Tabular Data Streams (http://en.wikipedia.org/wiki/Tabular_Data_Stream).
Now the question: Is all of this available as API? I don't know. Maybe. The fact is, however, that nobody uses them, and instead you connect to SQL Server using ADO or a simila technology.