There was only a single set of circumstances that would have allowed the Entente to force the Dardanelles: a surprise landing of a large number of troops (100-150,000 was the general consensus) on the peninsula to secure it. Once Gallipoli was secured, fast minesweepers would have cleared the minefields and allowed the battleships to reach the sea of Marmara with minimal losses. More importantly, the successful capture of the peninsula would have tipped the balance and it's most likely that both Bulgaria and Greece would have entered the war on the Entente side (or the danger of this intervention would have forced the Ottomans to sue for peace).
Unfortunately, none of the conditions were feasible: the element of surprise was lost in February by the untimely announcement of the operation, the fast minesweepers were never dispatched to the Aegean and (most importantly) there was not a single possibility that the British and French army commanders would have considered moving such a large number of troops away from the western front (Kitchener grudgingly considered a single division, the 29th).
The way the Gallipoli madness was carried out IOTL certainly precluded any possibility of success (fun fact: the telegram of Grand Duke Nicholas on January 2, 1915 asked for a "naval demonstration" against the Dardanelles as opposed to the grand strategy concocted by Churchill to win singlehandedly the war by a naval operation only). Even if Entente battleships had managed to reach the sea of Marmara (the most optimistic assessment was that no more than 4 BBs could succeed),what could have they done? These old BBs would have been low on coal and ammunition, and anyway Hankey noted that they could not have sustained a long bombardment due to the wear and tear in their main guns, not to mention that they would be without screening ships to manage the attacks of Turkish torpedo boats much less a sortie of the Goeben.
Gallipoli was Churchill's third brainchild (after Antwerp and Coronel) and a last desperate attempt to salvage his battered reputation as First Lord of the Admiralty.
For the fun of the thing, let's say that the set of conditions I outlined at the beginning are met, and the Entente secures the peninsula. It would be certainly a major coup: either the Ottomans sue for peace or Constantinople is taken by an army including Bulgarian and Greek troops. The Straits are open. I am not completely sure that it is enough to butterfly away the Russian revolution and subsequent collapse of the Czarist regime (it's certainly a boost of Russians capabilities, but not a get-out-of-jail card) but it is reasonable to believe that Russia will stay in the war at least until 1917.
OTOH there is quite a possibility that the Entente generals were in the right, and that by removing 100-150,000 seasoned troops from the Western front would allow the Germans to break through: it would not be a good bargain.
Overall, my gut feeling is that the CPs will be in a worse strategic position (for example, if Bulgaria is in the Entente, Serbia will not collapse in late 1915. A real offensive from the south Balkans may prove too much for A-H in 1916) and (assuming that the western front holds in 1915) a negotiated peace may be achieved in the same year. Maybe a whitish peace (Alsace Lorraine may have to be given away, and some colonies too) for Germany, but A-H will pay a much higher cost (although there is a chance that Charles might keep his crown, reigning over Austria, Slovenia, Bohemia and Hungary. Maybe Croatia too). The Pact of London should be upheld. The Ottomans will bled too (Thrace, Armenia and a good chunk of Eastern Anatolia may be lost) and the CUP will be disgraced, but the rest of the empire might be kept together, under some sort of protectorate.
IMHO it is quite likely they will keep Constantinople too, although it's not a given. Capitulations will not be rescinded.
A third Balkan war is however a given: Bulgaria, Greece and Serbia will find it difficult to stay away from it.
Shortening the war by a couple of years would be a big plus for anyone, and a negotiated peace treaty in 1916 would certainly be more sensible than the ones enforced in 1919.