There is nothing inherently different between an antenna and any old piece of metal. Many receiving antennae are of 'tuned length' but an office chair or a coathanger can also happen to resonate at a certain frequency. When this happens, more volts may appear at some point on it. You need to be very near to a high power source for this to worry you, however. Wire fences near high power broadcast transmitters can sometimes spark!
Remember, though, that the effect is not "static"; it is AC. Receivers always have some input resistance and may be 'matched' approximately, to optimise the received signal power so they are connected to a resistive load.
Spectrum analysers have much more gain than oscilloscopes, which incorporate wide band amplifiers. A spectrum analyser has very high gain but narrow band filtering and will select signals around one particular frequency and amplify them by many tens of dB - it is, in effect, a 'swept' radio receiver, whereas an oscilloscope is, essentially, a voltmeter with a graphical display showing how the total volts vary with time.