No that's the point, a radiation belt needs to be contained by "something". In the case of planets and stars it's the magnetic field they generate that does the containing, ions don't orbit, they travel in a straight line unless constrained by some force, and there is no such constraining force around a black hole because the only effect a black hole has on the universe is gravity. There is nothing around a black hole to hold the radiation in place to create a belt.
light travels in a straight line. ions have mass, which will be impacted by gravity, not just magnetic fields. Their speed can vary and they can be significantly slower than light (and thus at an orbit outside of the event horizon) while still being dangerous.
You're thinking of just light, em radiation, which at best could only orbit at the event horizon ...and that's not the only thing that comprises radiation in reference to radiation belts.
granted, gravity alone probably wouldn't allow such a belt to extend very far away from the event horizon.
A caveat though to this limitation is that the belt is not stable. But rather the result of a constant but tiny influx of matter from nearby stars (so this would be something that affects multi-star black hole systems) ... So you are experiencing an invisible sparse accretion disc with localized hazard as you near filaments of this orbiting matter falling towards the black hole.
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