Using an H-Bridge like a comparator
doesn't spin at all if the input voltages are equal


If the voltages are equal on a comparator, the comparator output is indeterminate - a comparator outputs 1 or 0 depending on inputs being greater than each other; when inputs are the same it won't output some constant mid range value.

Based on your understanding of comparators and my understanding of H bridges I'd say the answer to your question is no, a H bridge would not be easily made to behave like a comparator. If on the other hand to want to use two comparators (aka a window comparator) then the two outputs could control a H bridge to do what you want.