Cylinder size, as well as number, will affect the per-mile operating
cost - A 3 liter 6 cylinder (each cylinder half a liter) should (at
least in theory...) cost less per mile to operate than a hypothetical 4
cylinder engine with a total displacement of 4 liters. (Each cylinder a
full liter), regardless of the fuel it's burning.

Likewise, an 8 cylinder "monster" with a total displacement of 4 liters
would almost certainly run cheaper than a 6 cylinder with a total
displacement of 5 liters running at the same power output level.

Total displacement of the engine has a much larger impact on how
economical it will be to run the beast than number of cylinders, but
number of cylinders can't be completely ignored. This is due to other
factors such as the complexity of the additional machinery required to
handle more cylinders, increased parts-count, with attendant increase in
wear (and maintenance costs), mechanical drag caused by the additional
parts, and so on.

All of that said, though, when considered as a whole, an engine of a
given displacement will generally use fuel at *ABOUT* the same rate as
another engine with the same displacement, but a different number of
cylinders, when run at the same power-output level.

So, getting back to your actual question, yes, there is an effect from
differing cylinder counts, but outside the lab/off the dyno, the
difference isn't likely to be significant. It comes back to the basic
fact that to get "X" horsepower out of an engine, regardless of size or
cylinder count, you must burn "X" horsepower worth of fuel, whatever
that fuel may be, plus a bit more to overcome whatever
mechanical/frictional losses are inherent in the engine/drive train.