The MMX spacecraft does carry a radiation monitor that will be useful information for future crewed missions that may go to the Martian moons.
But IDEFIX is not designed to look for underground caves.
Exploring lava tubes has been proposed for future missions to our Moon. However, our Moon has a geological past that included volcanic activity that created lava tubes. Phobos is too squiffy for that, so I don't think we expect substantial caves.