Is it possible to generate a Sitecore zip installation package from a TDS project in a Visual Studio solution? Ideally, but not strictly, in a way that could run on a CI server.
I don't think there is a way to create a standard .zip package from within Visual Studio/TDS but you can do that with Sitecore Rocks and there is an example here by Trevor Campbell: https://community.sitecore.net/technical_blogs/b/trevor_campbell/posts/28-days-of-sitecore-rocks-package-creation. As seen in your answer to Joe, if that's all the functionality you really need, then that should be all you need to create a package easily from within Visual Studio. You can get Sitecore Rocks by going into Visual Studio and going to Tools--> Extensions and Updates --> Select Online --> Search for Sitecore Rocks. It should be the first selection in the list.
I use a mixture of Sitecore.Ship, TDS Update Package generation, and CURL to achieve CD from my CI servers.
Is there any reason why you want a zip package over an update package?