It's more a sci-fi way of expressing things, but yes, sort of. Time dilation becomes infinite at c, so massless particles do not "experience" time. This is the reason that photons on a Feynman diagram are traditionally drawn horizontally.

But the black hole part is actually wrong. Time dilation approaches infinity at the event horizon, not the singularity. So to extend your metaphor the interior of a black hole forever exists "beyond time" from our perspective.

Well, you can't reach c unless you're massless.

(Anything with non-zero mass would require infinite energy to reach c.)