You made me curious, since I too had noticed that hose the last time I replaced the cabin filter.
I just went out to the garage and had a look :
That hose ( and I assume you still have the hose, since it is in your picture ) does indeed supply air to the box inside the engine compartment where the RCM is, and it is NOT connected to anything at the lower end. Matter of fact, mine still has the factory tie-wrap on it, it just sucks air in from below the amplifier panel. although the service manual states it gets it's air from the cabin side of the filter.
( I guess it does, but not directly from the filter box )