Since I began this thread by suggesting that acquisition of the Straits played no part in Russia's war planning or decision making process in the July Crisis, I'm willing to make the leap that they expected their Entente partner, Great Britain to secure unfettered access to the Straits from Turkey for the Russian merchant fleet and hopefully her warships as well.
The Russian merchant ships could transit the Straits under the 1878 Treaty, it was the same treaty that closed it to Russian and other warships. Russia wanted this altered, but as Britain and France were the two nations who opposed her in this from 1878-1914 it was not something the Ottoman's really needed to be talked into.
Winston Churchill certainly can be cited as a statesman whose thinking and actions were heavily influenced by German activities in Turkey during the July Crisis.
Finding that Winston told everyone in his books in the 1920's that he considered things is a long way from him doing so at the time, and as far as I can recall the only question that arose was one that asked if the oil fuel needed for some of the RN was secure, to which the answer given was yes - and very few ships relied on oil for fuel entirely. He was even known to claim it was his idea to fuel the navy with oil, though ship designers and several staff officers had been suggesting it for some time, all Winston did was give it political approval. But then again we have the question did this fuel come from Abadan? The answer appears to be no, not entirely, though it was only access to this oil that had led the navy to agree to the Queen Elizabeth class being oil fired ships, as alternative supply sources were in place.
Grey and the entire Asquith cabinet must have had it in mind during their July deliberations, since the British concessions on the route were annouced in Parliament on the 28 of June.
The agreement had still to be signed and the track to be built even then, so why should it worry people during the July Crisis?
It is an oblique reference to be sure. But since it was a response to a heckler's questioning of how Germany could be 'our dear friend one day and our enemy the next', it clearly alluded to the generous concessions the Kaiser had given Britain on the Berlin to Baghdad Railroad exactly one month before.
So oblique as to make me, and no doubt many others, wonder why if this matter were really so key to the survival Britain or the empire it was not directly mentioned by any number of the more than six hundred people present? The comment looks somewhat more like one of the numerous comments from the time - the Kaiser really was Britain's friend and wouldnt invade Belgium, and if he did Britain still didnt have to go to war - that Britain should never have been making agreements with the Kaiser and how he and Germany were dangerous - how the Kaiser would never allow his military to really invade Belgium, it was all a ploy etc.
My professor of British history told me (and the rest of the class) "If you want to understand Britain's foreign and domestic policies for the 300 years prior to World War II, they must be viewed in relation to their benefit to the British Empire. Maintenance and promotion of the Empire was always first and everything else a distant second.
Hence the need for the Entente's (without them there was not the money or manpower to defend all of the Empire from all the varied threats), the need to prevent the most powerful continental neighbour with the second largest navy in the world establishing control over the Low Countries (the safety of Britain itself came before the empire and this issue had seen Britain at war, or at least in enmity, with every continental power to achieve this status for 300 years), the need to still keep Russian warships from the Med (this had been seen as late as 1909 when Britain and France both refused to support Russia in reopening this question, as it would allow Russia to pose a threat to Suez). Maybe after those you have the possible threat of Germany building a railway to Bahgdad, and given the time it had taken to get to Constantinople this was not a particularly immediate threat.