Can I break a radio tranceiving device by operating it with no antenna connected?
You could potentially break some radio transmitters by operating them without the antenna connected.

Several things combine to make this possible.

First, it's difficult to make power at RF frequencies, so the power devices are often fairly fragile, and run near their limiting conditions.

Secondly, radio signals passing down a transmission line behave in a way most non-engineers don't expect. They get reflected from an open circuit, that is, from a connector without the antenna connected. 

The antenna provides a load, absorbing the energy travelling down the transmission line from the power device to the antenna. If that energy is reflected, then for a well matched transmitter, it has the potential to double the voltage seen at the transmitting device. Depending on the length of the line, it might alternatively double the current, which usually isn't as bad. So a transistor that's already close to its limits could be pushed beyond them.

If the output device is poorly matched, then there's the potential for much higher voltage magnification.

Usually, the transmitter will be designed so that the power device is sufficiently within its ratings that it won't fail into any load, as blowing up into no load is not very nice behaviour. But sometimes, especially for low cost and high power amplifiers, like your CB kicker for instance, it won't be, and needs that load to prevent reflections.