The problem is that at the end of 1915 the CPs are ascendant: both the western front and the Italian front are stabilised (but the Germans are in occupation of Belgium and the fighting is inside France); Gallipoli has put an end to all hopes of a quick capitulation of the Ottomans (which means that the straits are closed for good, and no possibility for Russia to receive goods and export grain from the Black Sea); Serbia is gone; German victories in Eastern Prussia have pushed back the Russians, and the expectations for 1916 are not particularly good on that front. Wilson proposed to mediate in december 1915, and the response from the CPs was not negative (no surprise); the Entente was quite adamant in refusing any talk (spearheaded by the French). Pope Benedict made his efforts mainly in 1917, if I'm not wrong: however, he would have certainly supported a peace initiative.
We've been already discussing this POD in other threads: any peace agreement in late 1915-early 1916 would have resulted in an effective defeat of the Entente, whatever the actual peace treaty reads. No chance that France gets back A-L (not even a chance to go for a referendum): A-L are the landmark of the German empire, and giving them away it would be considered a big loss of face in Germany. Serbia is out of the war: any peace agreement would see it as the big loser. Probably it would end up loosing a big chunk of Macedonia to Bulgaria, with the rump Serbia turning into an A-H puppet. This would effectively turn the Balkans into an Austrian protectorate, and - together with the Ottomans being firmly in the CP field - would definitely threaten British interests in SE Persia. The political backlash in France would be awful: the government would certainly fall, and there would be riots and general strikes. I'm not forecasting any "red France" here, but a military coup could not be discounted: this TL would be likely to see a reactionary and revanchist France, with the Action Francais playing a big role: I'll go a step forward, and assume that here the myth of the betrayal of the otherland by Jews and Socialists would be a French refrain, not a German one. It is likely that socialist strikes will extend to Italy too, even if the situation there should be less complicated than in France (and the end result might be a moderate socialist government). The situation in UK is likely to be somehow complicated: even assuming that Belgium is restored (and even some compensation is paid by the Germans) the settlement will not be considered a victory and might even convince the Irish that the British government is weak. Bloody Easter is still in the cards.
Russia: the cheapest price they will pay will be an independent Poland, in the CPs's sphere of influence. There will be some significant political backlash there too (it is the second war in a row which goes badly, and Russian losses have not been insignificant). Riots and strikes will happen for sure; IMO, the czarist regime will hold, but will be forced to make some concessions to the Duma (and Nicholas might be forced to abdicate, to be replaced by his uncle).
Imperial germany will try and sell the result as a victory (which is partly true); still I'd anticipate that the german socialist will benefit too from the peace, and - just possibly - that Germany will slowly move toward a more democratic regime. A-H and Turkey will enjoy the greatest benefits: once again, it will look like a victory, and will strengthen both (internally at least).
IMHO, I'm quite confident in the Ottomans continuing with renewed will in the political and social reforms supported by the Young Turks (there is the risk of an increase of pan-Turkism, which would effectively restrict the benefits of the reform to Istanbul and Anatolia, leaving the arabs very unsatisfied): this, together with the economic benefits of the Berlin-to-Bagdad railway and of the development of Mosul oil fields, might have very beneficial effects for Turkey. I'd be a bit more cautious with the after-effects in A-H: the "quasi-victory" and the humbling of Serbia will have a positive effect for sure, but it might effectively delay the much-needed reform of the empire (still Karl is scheduled to be emperor in one year: he is likely to be in favor of reforms).
Overall, both Europe and ME would significantly benefit with an early peace (even factoring in the political unrest and the unavoidable economic slump, while the heavy industry is phased down): TTL should be able to avoid WW2 and the fascism (and quite likely communism too), and is likely to be more democratic; the Irish might end up much worse than OTL. The difficulty is in convincing UK and France (mostly France) that the war has to end.