Let's forget the word "interference" for a minute ... for example in a double slit experiment (DSE) we know there is no cancellation of energy (that's a violation of conservation of energy). In the DSE we do know that all photons/light appear in the bright bands, there is no energy or photons in the dark bands.
Now let's take a simple laser, i.e. excited photons between 2 mirrors where the mirrors are placed at exactly an integer number of wavelengths apart. There will be no energy transmission until one of the mirrors is say typically made only 90% reflective and 10% transmissive .... then the light emerges and the cavity is able to continuously convert electrical (typical laser diode) energy into light.
Now if you put an external mirror in front of the laser you will find that the laser stops emitting light ... verifiable as the laser diode current say drops from one amp to maybe a few milliamps .... the external mirror just becomes an extension on the laser cavity.
So your experiment will result in the same behaviour within the frame of reference of the laser (typically a train or spaceship). The classical "interference" is present, no light is visible, but in reality the "interference" is a result of the photons not having a suitable/path to follow. This is Quantum Optics, or another approach is what Feynman used, all paths are considered but in the end the shortest path that is n times wavelength is most probable for light/photons to propagate.