Yes, the air from the room below will flow upwards through the slats because the average pressure at ceiling level in that room will be greater than the pressure of the air at floor level in the attic. The lower average density of the attic air will result in the pressure at attic floor level being somewhat less than atmospheric at the same altitude whereas the attic pressure against the roof will be somewhat above atmospheric at any given height.

I've used the term "average" to mean the dynamic equilibrium pressure in the absence of sudden flare-ups, from non-steady state phenomena which are common in normal fires.