There is often an interface between the lens and camera. It's different for each camera maker usually. It may be mechanical, electronic, or both. It may provide

There is often an interface between the lens and camera. It's different for each camera maker usually. It may be mechanical, electronic, or both. It may provide significant power to the lens, a data path for firmware updates (Olympus), or even mechanical rotation to drive unpowered focus mechanics in the lens (Nikon). Various lens parameters can be communicated to the camera, including static lens capabilities but also dynamic factors such as the current manual focus distance, current manual aperture, or focus mode. So yes, they could do that. But some systems would be designed with the assumption that all lenses will have shutters, or that the user of lenses with shutters will set the camera shutter to remain open. Sometimes the shutter release "button" is part of the lens instead of the camera.