You would have a lot less trouble if you put in some middleware like kbmMW, Remote Objects, or DataSnap. All of them can use plain TCP/IP (via http or like higher level protocol), and don't require client side libs. You will need an extra server, but it is easy to create one that just forwards your SQL and data between clients and SQL server. Note that SQL server licensing remains.
On the other hand, you can try to install SQL Server native client, some older version of it - eg. for SQL Server 2005, in that "bottle" with your application. Yet, I'm not sure if that is legal thing to do. I think that MS prohibits native client installation on OS other than Windows.
There is FreeTDS native client that works with MSSQL from unices, but it is not ported to be usable from Delphi (like dbx driver).