In packed beds that I've seen, the pressure loss across the bed is miniscule compared to the absolute pressure (on the order of 2%), and the length of the packed bed is sometimes 2 or 3 diameters (or more). Finally, the gas is usually undergoing a chemical reaction (which is generally exothermic).
Looking over the net result of all of these effects:
1.) Pressure drops by 2%, which could increase specific volume or temperature
2.) Gas passes through long, uninsulated column which maintains gas temperature at or around original temperature, resulting in temperature to return to normal while maintaining density decrease
3.) Gas absorbs substantial heat from chemical interactions, which dominates the two effects above, resulting in temperature increase and an altogether different gas state which has reduced pressure (if pressure increases, the gas won't flow), with likely higher specific volume and higher temperature.
If only for effects 1 and 2, I'd argue that a packed bed results in a change in density, because the gradual temperature change is removed from the long travel length. However the final effect changes things to a chemical engineering problem.