Without a martyred Gordon (the British public would probably ignore the killing of the Egyptian Army, the European traders etc in Khartorum and Sudan that followed the mahadist takeover) the British Empire may chose to involve itself less in Egypt than it did. IOTL Egypt was modernized and armed (as described by Kipling in "Pharaoh and the Sergeant" -
http://www.poetryloverspage.com/poets/kipling/pharaoh_and_sergeant.html) to stand against any potential Mahdi aggression.
On the other hand - Britain was determined to keep the Suez channel, and any Mahdi attack would be a danger. To let "natives" defeat the Empire, even Egyptians that were clients of the Emipre, was dangerous because other "natives" could get ideas of rebellion. So a British campaign against the mahadists were probably determined no matter Gordons fate - and using Egyptians were the most cost-efficient way.
Gordon would be toast for disobeying orders - but several heads could roll with his. Both the political and military leadership were on purpose very vague about his mission, which could lead to several types of political crises.
Just two big potential butterflies: Churchill made a lot of first impressions from the campaign against the Mahdis in 1898, not only the battle of Omdurman but also his first book, "The River War". Secondly the Fashoda incident partly went peacefully since the British arrived at Fashoda directly after Omdurman with overwhelmingly superiority. Otherwise it could have ended far less aminiable.