Re: Comparator design
Theoretically, yes, if the input stages gets saturated by DC, then the whole mechanism collapse.
In practice, comparator are not totally the same as opamp in that
we often add differential type cross-coupled latch stage before digital output buffer. And even in cases where input differential pair is not really in linear region we can get correct result since with cross coupled latch, never two output (positive / negative) shall both stay at same logic level (high / low).
Only thing to watch out is how much time it takes to resolve the difference of input signal level difference when it comes to small as mV.
Hope it helps,