reference: Microsoft XNA Licensing

Quote: The Microsoft XNA Framework 2.0 EULA specifically prohibits the distribution of commercial networked games that connect to Xbox Live and/or Games for Windows Live in the absence of a specific agreement signed by both you and Microsoft.[13] This means that XNA Game Studio can still be used to develop commercial games and other programs for the Windows platform, although Microsoft's networking support code for Xbox/Windows Live cannot be used. Self-developed network code can still be used inside your XNA project. Games created using XNA Game studio may now be distributed via Xbox Live Community Games. The software may also be used to create commercial games which target Windows.

Does this mean that as long as I am using TCP (over the Internet) and not explicitly connecting to "Windows Live" for client-server gaming applications, I am not in violation of the EULA?

I think you are right - as long as you are not using the XNA Live networking stuff, you are free to distribute it however you want.