The antennas generally are multi-purpose, also serving your navigation and sattelite radio, so covering the antenna may not be idea. However, there are usually multiple coax coming away from there, and they route to the appropriate modules, and can likely be disconnected there. It varies widely between manufacturers and generation. The antennas are powered and there is usually an antenna protector device in the module which supplies power to the antenna (bias T). These use a part which is current limited and also can have open and short circuit detection so disconnecting the antenna can give you more than just a "no signal" error.
In current architectures we are reaching the point where it is so thoroughly integrated with the vehicle that it's not possible to disable it without significant inconvenience, or worse. For the last 10-15 years, the telematics/infotainment module has been the home for the most powerful microprocessor in the vehicle, and this caused more and more functionality to be pulled into this module.
I'm surprised that there is not more hacking done of these modules. On many of the newer vehicles there are options you can unlock - Such as bluetooth - That the OEM wants you to pay for much like the scope options people are hacking on here.
It would be great to see some people put their passion into thoroughly analyzing and publicly documenting these architectures. Most people "in the know" are under perpetual NDA (or worse) and really can't talk about specifics at all and can only make general statements.
Every infotainment system has various test modes/systemaccess method present, either used for diagnosis when a module is sent back to the factory, or remaining from the development phase. A majority are running some flavor of linux. Access is generally via a USB port on the module (that is not connected to a harness like the other USB port(s) in the vehicle), or through one of the USB ports in the vehicle (if there are multiple, generally only one can be used to access the system), or through a USB to Ethernet adaptor. Or any/all of the above. Some have secret keypress combinations to open up a port or boot the infotainment system in a way that enables access but I'm sure people can figure it out. Would love to see it.