Only the first three smoke stacks were actually connected to the furnaces that produced the smoke. The fourth smoke stack was, in a sense, a dummy stack.
I believe that it wasn't entirely for show, to give the ship pleasant lines. If I remember correctly, it contained air vents, a fireman's ladder right to the top and I even hear it had some 'emergency dynamos' built into it's base.
But, yes, it was a false stack in the real sense...
The fourth funnel provided air ventilation for the
galleys as well as a chimney flue for the 1st
class smoking room. Smoke and/or steam would emit
from the funnel, but would be hardly noticable,
especially when compared to the first three
stacks, which were connected directly to the
boiler rooms. The smokestack did have a ladder to
its top, as evidenced by the famous stern-on shot
of the Titanic at Queenstown. You can see a stoker
poking his head over the top of the 4th funnel.
The 4th funnel was indeed a fake if you get a chance to read the book Last Days of the Titanic then you will see in a photo of the ship in Queenstown that a small black dot is on the top of the funnel and it is actually a stoker who came up for air. The original plans called for only three funnels to be seen on the ship there would be no 4th however Lord Pirre added the 4th because in those days a ship with four funnels was the symbol of a safe ship.
Don't forget symmetry and Cunard. Mauretania and Lusitania (pretty much the main reasons why the Olympic Class vessels were conceived) had four funnels. WHITE STAR WASN'T GOING ONE LESS! That simply wouldn't be cricket. The "Edwardian" era just had a thing against odd numbers.
For all intents and purposes, the functions of the fourth funnel could have been spread over the first three. Last I heard, the only practical use for that funnel was to store excess deckchairs!
Deck chairs weren't stored in the base of Titanic's fourth funnel. You might be thinking of Normandie (and I think Queen Mary, too, though my memory falters on that one)
I remember seeing a cross section of the fourth funnel somewhere. Dan Cherry might know where it could be at.
Titanic's fourth funnel was capped off because there wasn't any need for it to be open. The first three were open to allow exhaust smoke from the boilers to be released. The fourth only needed enough open to allow for galley uptakes and ventilation (refer to Dan's post above).
The cap over the fourth funnel was probably just to keep the rest of the funnel from filling up with rainwater. As for the bars crossing the foreward three funnels, I'm not totally sure. Lusitania and Mauretania didn't have them. I'd imagine that they provided extra support for weather covers while the ship was in port (See the famous photo of Normandie and the Queens tied up in New York in the '40's. Normandie's foreward two and all three of Queen Mary's funnels have a weather cover in place) The cover was to prevent rain water from getting into the ship while sitting idle in port.
Looking at Titanic's deck plans in E&H aft of the Turbine Engine Casing whose outlet was into the 4th funnel there were 4 small rooms leading off of the Raised Roof of the 1st Class Smoking Room. The after starboard room is marked: Deck Chairs. This places the deck chair storage area within the raised area which forms the base/surround of the 4th funnel. You can see a view of it in: The Titanic Revealed on page 50 of Don Lynch's: Titanic An Illustrated History.
In reference to what you were saying about soot and ash coming out of the funnels, the angle or rake of the funnels took most of what little solid matter that came out and fed it to the wind at that height which would have taken it back behind the ship before it had time to land on deck. Straight vertical funnels do not really provide this.
Besides, any ash from the funnels (at their angle) that happened to land would have touched down on the poop deck mostly, and which class of passengers on board use the poop deck most we wonder? A small price to pay for White Star Line and their image.
The majority of the ash was taken care of by the ash ejectors which I believe sent most of the ash into the sea along the sides of the hull