The important point is once a pixel is saturated it won’t count any more photons. It is possible that if a tiny number pixels are just above saturation or in the non-linear region then that non-linearity won’t be obvious. There will be lots of pixels contributing. However, it is a risk and you would not be able to justify your result if you were trying to extract a reliable magnitude.
Looking at your graphs, they show a slightly different behaviour in the linear region. It appears to be a steeper slop, followed by a little bit of a wiggle.
If saturation is a problem as you want longer exposures then you can slightly defocus the star. This will spread the photons over more pixels while keeping them within the linear region.