It's difficult to say. The two contemporary sources that provide the historical account - Thucydides and Xenophon - both credit Alkibiades with enormous personal influence. In their works, every single new idea embarked upon by Athens, Sparta and Persia ultimately has its source with Alkibiades. When a single person is given this much of a role, we should be careful not to take the account at face value too easily - but it is difficult to disentangle fact from fiction without an independent source.
According to Thucydides, it was Alkibiades who had a viable plan for the subjugation of Sicily; his flight and exile therefore indirectly led to the annihilation of the expeditionary force at Syracuse, the greatest defeat suffered by Athens during the war and a disaster that did more to accelerate the eventual Athenian defeat than any other before the final defeat at Aigospotamoi in 405. More directly, Thucydides claims it was Alkibiades who gave the Spartans the idea to build a permanent fortress in Athenian territory. The fortification of Dekeleia ended up a constant drain on Athenian military and economic strength. He was also supposedly the one who first encouraged the Spartans to court the Persians for financial support, and the only Greek who had the connections (or so he claimed) to get them to pay up.
Now, if Thucydides is right, and Alkibiades initiated both these strategies, he may rightly be said to have masterminded the downfall of Athens. He eventually turned coat again and helped Athens temporarily recover much of its overseas dominions, but this was largely in vain. Even Alkibiades could not accomplish much in light of the fact that Persian funding made the Spartan fleet a Hydra - whenever it was destroyed, it immediately reappeared - and the fact that the fortress at Dekeleia prevented the Athenians from ever dropping their guard or diverting additional funds into their navy. His two ideas in combination proved fatal to Athens.
However, it's fair to ask whether it is really likely that the Spartans needed to have both war-winning stategies spelled out to them - and by an Athenian no less. Tellingly, Thucydides has both the Corinthians and Perikles anticipate the strategy of epiteichismos, the construction of a fortress in enemy territory, before the war had even broken out (Thuc. 1.122.1, 1.142.2). It is of course possible that he added these comments in at a later point in the war, when it had become clear how devastating this strategy was for Athens; but even if no one saw epiteichismos coming in 431 BC, there would have been no further doubt about its effectiveness after the Athenian fortification of Pylos and capture of Kythera in 425 BC. The Spartans surely didn't need Alkibiades to suggest to them that they should do what they could see the Athenians doing with their own eyes.
It is not clear why Thucydides makes Alkibiades so prominent in defining Spartan strategy after his exile, when he hardly seems to be a big fan of him elsewhere. It is Alkibiades' demagoguery that convinces the Athenians to set out for Sicily, which Thucydides treats as an unmitigated folly. Perhaps the explanation is in the fact that Thucydides consistently characterises the Athenians as quick-thinking innovators and the Spartans as slow-moving conservatives. Within this paradigm, the shift in Spartan strategy at the start of the Dekeleian War could more easily be justified if it was an Athenian who gave them the idea. In any case, the influence of Alkibiades is almost certainly overstated. With the loss of half the Athenian fleet at Syracuse, it was clear which way the fortunes of war were leaning. In addition, despite his boasting, Alkibiades could not secure a reliable flow of Persian money until the Spartans found a willing ally in Kyros.
Something similar can be said about Alkibiades' role upon his betrayal of the Spartan cause. While Xenophon relates Alkibiades' successes with a great deal of respect, he emphasises that he was a controversial figure. On Alkibiades' return to Athens, Xenophon makes it clear that there were plenty among the crowd who disapproved of the decision to revoke his exile. In many of the events of the latter stages of the war, his role is actually quite immaterial; he achieved a number of things, but suffered a defeat at Notion through neglect, and generally failed to affect the downward trend of Athenian power.