Assuming you specify TCP protocol, is it possible to bind your SqlConnection to a local IP end point in the same way that you would a socket? (Is there an underlying socket for a TCP SqlConnection that I can access somehow?)
The goal is to force the connection to be made with a specific network adapter on a machine that potentially has multiple. I'm sure the first natural question will be "why" in an effort to point out alternative solutions, but I am not seeking alternatives. I simply want to know if this, specifically, is possible. Thank you.
That's really what routing tables are for. If your network adapters are correctly configured, there's no need for you to handle this on the application level.
That said, SqlConnection doesn't even have to use Sockets in the first place - it's the common class handling whatever connection to the SQL server that's possible. This can be a direct socket connection or a named pipe, for example. The connection can also be pooled.
There's no setting in the connection string that would allow you to do this. And that pretty much ends any reasonable way of forcing a local endpoint for the socket connection. This shouldn't really be all that surprising, since applications shouldn't handle stuff like that at all.
Going through the relevant sources, it's obvious that even when there is in fact a socket, it's not a .NET Socket - so there really isn't any way for you to influence this even using reflection, for example. The only way that remains is to install a DLL hook on winsock (or perhaps the SQL client DLL) and intercept the connect call; of course, this is quite a desperate move, and will cause you tons of trouble if you try - not to mention that it requires the use of native code, and that it's incredibly brittle (and bound to cause trouble for other applications as well, not just yours).
There's definitely better ways to handle your scenario. But since you're not looking for alternatives, this is the best I've got.