I don't know if this is even a feasible question or if I have a point in asking so.
Let's say we can model the radiation coming from a very compact object, such as a BH with an accretion disc or any star with proper dimensions (for example, with its disc/gravitational radius within its photon sphere $R_\gamma = 1.5 R_s=3M$), as a black body radiating isotropically. I guess we can do so, since we cannot imagine any good reason for discarding this approximation in them!
What I try to ask is basically if we should modify the formula for blackbody emission or whatsoever bolometric magnitude/luminosity in such an object, given that we already know a radius and an effective temperature (we are using $L = 4\pi \sigma R^2T^4$ here). And also considering that due to the strong curvature some photons emitted in the surface of the disc/atmosphere will be returning inside and will never reach us...
when measuring the subtended emission angles from a local static observer.
What I'm sure to know and explain with my own words is that the emitted photon flux reduces when we measure it as receivers on Earth, due to this capture.