Could micro black holes obey the Eddington limit?

A stellar-mass black hole has recently been discovered in the Andromeda galaxy. One interesting part of the release is that this black hole shines close to its Eddington limit.

Quasars are supermassive black holes shining at or near the Eddington luminosity, and microquasars are likely stellar-mass black holes whose accretion is similarly close to the theoretical maximum.

Wikipedia derives the equation for the Eddington limit (although I'm not sure about the applicability of its assumptions to small black holes) to be proportional to $M$. The Hawking radiation from a black hole goes as $1/M^2$. This implies that a cross-over point where both formulas calculate the same power. I can calculate this to be about $4 \times 10^{10} kg$.

What would be an accurate picture of a micro black hole, given sufficient matter around to feed it? I think that the Eddington limit is a balance between the gravitational pull and the radiation pressure, but in the case where Hawking radiation is present, would the picture be significantly different?

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