tl;dr: no, and the issue here is that gravitons probably aren't like what you're thinking. (and it's not a dumb question). In perturbatively quantized gravity

tl;dr: no, and the issue here is that gravitons probably aren't like what you're thinking. (and it's not a dumb question). In perturbatively quantized gravity, we start with a background metric (e.g. Minkowski flat spacetime or Schwarzschild black hole spacetime) and then "perturb" it with other moving matter. With a careful choice of slicing of the 4-spacetime into 3+1 space+time, we can see the (leading order) deviations from the background metric as a plane wave propagating lightlike from one spacelike slice to the next. Quantizing those waves in much the same way as we quantize classical electromagnetic planar waves leads to the graviton as a massless boson (but with spin-2 instead of spin-1). A spherically symmetric non-rotating black hole (and having factored out changes in coordinate position and linear momentum by choice of coordinates) sources exactly the Schwarzschild metric, so there is no perturbation from a Schwarzschild background (and thus no gravitational waves to quantize, and thus no gravitons in the vincinity). If we throw something into it, there will be a perturbation of the exterior metric, and thus gravitons in principle observable outside the horizon. There are theories that define a graviton, and the result ought to be the same: you generally only get (real rather than virtual) gravitons when something is falling into a (maximally symmetric) black hole (and very shortly afterwards, during "balding"), or: If you break the Schwarzschild symmetries by adding angular momentum and/or charge to the black hole, you can also get perturbations of a well-chosen background metric, although extremely little gravitational radiation (and thus few gravitons) unless something massive is sufficiently near the black hole. But just to repeat: an isolated non-rotating black hole emits no gravitons. You need to perturb it out of its highly symmetrical state in order to get gravitons. [cf. https://en.wikipedia.org/wiki/Gravitational_wave?oldformat=true#Sources https://en.wikipedia.org/wiki/Gravitational_wave?oldformat=t... -- for a black hole the relevant configurations are a significant "bump" on an otherwise highly symmetric black hole or a significant mass creating a "barbell" style binary]