Stability of delta sigma modulator with high frequency signal input
There are no stability problems if the spectrum of a reasonable amplitude input signal extends into the 'noisy' region. The converter is stable in the presence of large voltage swings there anyway, a little extra additive input makes little difference.

With enough amplitude, it is possible to overload a sigma delta modulator, but this is just normal behaviour, any device has an overload level.

Given that the signal recovery filter after a sigma delta modulator removes, essentially completely, all the noisy region of the spectrum, it would be possible to overload the converter and not realise it, if looking at the filtered output signal alone.