Are these at all likely to bring Bulgaria in before the Gorlice-Tarnow breakthrough (May 2)? Once that starts the Bulgars are likely to wait and see, and once the extent of its success becomes clear they are far less likely to join what might prove to be a losing side.
I don't think so. I think that the Bulgarian decision would be sway-able only by factors right next door to them, like the fighting in Serbia or a hypothetical Entente success in the straits. A rollback of the Ottomans to the Taurus mountains, even with the withering and loss of Ottoman territory south of the Taurus, won't be seen as too relevant in Sofia.
An early sweep of the Ottoman out of the Arab lands can be a blessing for the Allies regardless. If they win in Palestine, Syria and Iraq early, well, they don't need to keep trying to win on those fronts. If things turn into a stalemate in southern Anatolia, the Western Allies can possibly remove some of their troops to other fronts. I would think that if the Anatolian heartland is being pressed from the south, the Russians do not need to use as many forces as they did to defend in the Caucasus, or to attack, which maybe helps them some elsewhere.
An early sweep of the Ottomans out of the Arab lands could also be a bit of a poisoned chalice. The British would have to deal with the politics of Ottoman succession and occupation in those regions, possibly facing multiple revolts that the Germans and Turks won't even need to pay for. There could be a lot of political energy and policing costs expended, as well as chances for the British and French to build up mistrust or envy.