If it were true that buying one player guarantees you the league, I think we would have bought said player by now, but it isn't true, never has been and never will be I'm afraid
Nothing is guaranteed but getting him significantly increases our chances of winning the league. If we got RVP instead of the rags that year as planned I'm pretty sure we would of won it as well.
Sanchez is one of the best players in the league not only scores but also creates. On top of that he never stops running and is a menace when pressing. Last season if Arsenal didn't have him they would of finished behind Everton. He had a hand in about 44% of Arsenal's league goals if I remember correctly. He put the whole team on his back countless times, won games by himself when everyone else went hiding.