Interesting question so I did a some back of envelope calcs which may or may not be right.
First assumption is that you expose each sub to 10x the square of read noise so you are shot noise limited.
So lets say you have a 2e- RN camera, you expose the sky background to 40e-.
That background will have its own shot noise of sqrt(40) or 3.6e-
Now lets treat the sky background as noise rather than signal and I'm not sure whether it adds to shot noise in quadrature or by addition. Some more learned forumers may enlighten us on that. I've guessed it is in quadrature so sqrt(40^2 + 3.6^2) = 40.5e-
Next it depends on how much you stack. Stacking reduces noise by sqrt(N) so a stack of 100 would reduce the noise by a factor of 10 to 4e-
This article
https://www.dspguide.com/ch25/3.htm indicates that the minimum contrast needs to be at least equal to the noise so you'd need a target signal of 4e- in the example.
If we take that as a ratio of the sky background that's also a factor of about 10 or roughly 2.5 magnitudes. That is, an object 2.5 magnitudes dimmer than the sky background will be discernible after stacking 100 subs. If the noise doesn't add in quadrature the result is different. More stacked subs will enable dimmer targets and vice versa.