They do not specifically turn on/off any page features. However some themes do not support custom page types and thus limit admin sidebar elements, widgets, comments, reply blocks, and other features to built-in WordPress page types.
That is going to be more & more of an issue as there are a lot of plugins, themes, and even WordPress object types that are using the custom page types & taxonomies system.
If we find a way to trick themes into processing the page types we will build it in. Also, post your theme URL so we can play with it on our dev servers and look for workarounds.