That's really hard to answer without knowing the details. For sure
there will be oil evaporating and depositing on the wall. However, if
you happen to put wet things in there can be big bursts of spattering
as the steam comes out, and those might carry even more oil up.
Obviously, you could do controlled experiments to find out. You
could take a smooth glass plate at a fixed distance from the fryer, and
compare buildup on it with just hot oil or with hot oil plus some
For a first guess, you might look at the pattern of how the oil
coats the wall. Evaporated oil will go pretty far. Spattered oil won't
go so far. You could look at the spattering, then see if the oil
coating extends out much farther.
I had a roommate once who coated the kitchen with thick oily gunk.
We bought a filter unit, which helped some. A real exhaust system would
have been better.
(published on 10/22/2007)