What happens if a series of EM waves pass through an inductor?
Two answers:

Yes, you're describing a "loop antenna."   A loop antenna is simply an unshielded inductor that's being used to absorb some incoming EM waves.  In non-radio circuitry inductors are shielded to prevent this from happening.  Shielding can take the form of a ring-shaped toroid core, or an "E/I" shape core with the coil inside the slots, or simply enclose the inductor (or the entire pcb) in a conductive shell.

Besides loop antennas, another "inductor-like" antenna is the end-fire helix, where radio waves come in towards the end of the spiral, and are guided into the coax cable.  Helical antennas are commonly used for satellite comms, since they're inherently circular-polarized, and will pick up signals from distant dipole antennas at any random alignment.



Second answer: can waves pass through inductors?  Yes and no, because whenever a component is large enough that EM waves can fit inside, that component isn't a capacitor/resistor/inductor anymore.  Instead it has become a waveguide element.

For example, at high enough frequencies, a parallel-plate capacitor is no longer a capacitor, instead it's a halfwave resonator.   And with short enough wavelengths, all your wires become antennas.

An inductor, if wound single-layer on a cylinder core, can have several EM waves moving across it, because it has become a helical waveguide.   (Actually that's the basis of Tesla coil secondaries: they're quarter-wave helical waveguides, with one end grounded, and driven at a frequency where a reflecting wave builds up.  Like an organ-pipe, but for EM waves.)

The key point here is this: for normal circuitry (small components and long EM waves,) the "Waves" instead behave as AC b-fields and e-fields.  They simply become our familiar AC volts and amps.

On the other hand, if the first part of a wave is still on its way through a component, while the next part of the wave changes polarity, then at least one halfwave can fit inside that component, and it no longer behaves as expected.

Another way to say it:  inductors and capacitors must be small enough to remain well inside the "nearfield" zone where "nearfield" is a quarter wavelength at your operating frequency.  For example, at 2.5GHz wifi microwave, the "nearfield" is about an inch.  If your wifi component isn't far smaller than one inch, then it's starting to become all waveguide-y inside.  Instead try 10MHz circuitry, where electronic components won't act weird, as long as they're far less than 25ft long!