Alexios was probably the last good general that the Roman Empire (Although calling that pitiful state an Empire is sort of laughable). But he can't save the Empire.
Although a good portion of the Ionian coast and Bithynia are still in Roman hands, they have been weakened by war. Also, Alexios's campaign wasn't against the Ottomans (Who weren't, mistakenly, considered a serious threat. Instead, his campaign was against the Beydom of Menteshe, who was a naval threat to Roman power.
The best chance for the Empire, although probably little better, is for Alexios to instead be successful in seizing the throne. The problem with Andronicus is that he was an extremely weak and incompetant ruler who neglected the defenses of Asia. But he did so to strengthen his hold on Europe, because the Bulgarians and the Serbs were seen as a greater threat.
It is likely that Osman still takes Bithynia, and solidifies his control of some of the more productive areas of Asia Minor. The Romans just simply had too many enemies, and not enough resources. Osman is probably one of the greatest generals of the Medieval Era as well.