No. In fact, the entire observable universe is a black hole: the Schwarzschild radius of the mass of the observable universe is greater than the observable size, meaning by the technical definition of a black hole we are living within one: light from Earth sent into the darkest region of the sky will not escape the gravitational pull of the whole universe, even before considering expansion rates.

The Schwarzschild radius for the mass of the observable universe is about 13.7 Billion Light Years while the observable universe is about 93 Billion Light Years across (radius ~46 Billion Light Years). So the universe is not itself a black hole (until you take expansion rates into account)

I think you have that backwards--you have to take expansion into account for the "observable" universe to be that large, since the age of the universe is only 13.7 billion years.

The Eddington limit constrains the absorption rate of a black hole, but through mergers there's no theoretical upper limit.

Aside from the useless limit of "all the mass in the universe"