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I am assuming you mean for logic signals? The answer is yes. You will need to have a decent amount of hysteresis though. But why would you do that? The comparator cannot switch as fast a logic inverter. The comparator is essentially an op amp slowed way down (heavily internally compensated plus some extra goodies). But alas, you can buy comparators with push-pull output stages that switch in about 10ns which is fast! But, the logic inverter is faster!
Well, maybe you are wondering because in your design you have a spare comparator but you need an inverter so why not use it? well, you will have to add a few extra parts to make it work so instead, just add a real inverter (you can get singles from fairchild and National - See tiny logic series)
If it can be crude, just make a discrete inverter using a transistor and a couple of resistors. I promise you can make one that switches faster than most comparators and it is cheap.