Voltage reference for comparator
Can I expect a significant advantage from using precision reference in my application?


Yes. The power supply rejection and stability of a precision voltage reference will be, by design, much superior to a voltage regulator. If not, you've got a rubbish voltage reference.

No, will it be useful/necessary?

Without knowing more about your situation, it's not clear. You need to determine exactly how much noise you can tolerate and how much stability you require. As long as your regulator is relatively stable, a voltage regulator and a decoupling cap should be sufficient for most applications.