The stars need to be rendered behind everything else in the game: Ground, planes, atmosphere, clouds, effects etc. etc, so it needs to have the highest (or lowest) Z-value, meaning it has the biggest depth.
Discussing hemisphere size is not really a fruitful topic. If you put a model of finite dimensions "around" the game environment, you will still move relative to it, so unless you make it, like, tens of thousands of kilometres in diameter you will get distortion effects when you move "closer" to one side of the box.
Skybox background is usually defined as a model whose location is fixed to the camera, but orientation is fixed to the game world. That means when camera moves in the scene, it is always at the centre of the background and thus the rendering of the background doesn't change; it remains constant. Thus, the actual dimensions of the starfield model can be anything at all; what matters is the Z-value it is rendered with, because with 3D rendering you can do tricks like render the background first - no matter what DISTANCE it's at, then render all the other stuff in front of it and the background will poke through the "empty bits" denoted by alpha channel.
What I have in mind is basically stars on black background, which would be rendered with Z-value preceding everything else in the game. The game would then render its environment, atmosphere, etc. and ideally during day time, the bright atmosphere would naturally block out the stars just like how it happens in reality. When you climb to higher altitudes and the sky becomes darker you start seeing more stars. When it's night the atmosphere darkens even further.
I have no doubt that if this were possible, it would be absolutely incredible to fly during night-time, evenings, mornings, or high altitude. I have the assets and skills to create the background textures, but applying it on IL-2 is another matter altogether.
Any opinions on whether it's possible to do this way?
A VERY LARGE background model is an acceptable substitute but harder to manage. I have no idea how large models IL-2 supports, either.