They were doing well in Anatolia without Brusilov there, the problem was logistics and lack of equipment. So even if commanders received the reinforcements they needed, they couldn't supply them far from border due to adverse terrain.
What about a 1916 Russian amphibious landing directed at Constantinople?
Yes, but I don't think there was ever a possibility of Russia conquering Anatolia.
Had Russia avoided losing WWI, it could have at least insisted that the Sykes-Picot-Sazonov Agreement also allow it to annex central Anatolia, no?