The fact that there is a KO vessel in that location indicates that someone thinks that liquid entry into the incenerator isn't a good thing. The KO pot is to remove liquids, and especially slugs of liquids that it sees. The demister pad is to prevent carryover from the KO vessel during the separation process. All things being equal I would use the demister.
Since a KOD is usually designed to separate a certain size of liquid droplets (vg 300-500 micron), besides slugs of liquid, I found redundat to install a demister.
Also, if the gas stream is expected to be dirty then demister can be plugged causing a great undesirable pressure drop.
I agree with jeap's comment about possible demister fouling if it gets dirty. If you're dealing with a clean vapor-liquid system, the demister can be very effective in helping to eliminate carryover. In fact the "k value" in the famous Brown-Sauder equation for sizing K.O. Drums can be doubled with a normal 6" mesh demister. That's a pretty big deal, since it means you need only half the cross-sectional area in the drum.
Doug