Rumors of the King's death were spreading before it was used to win the day, the whole Swedish centre broke after a disastorous charge. Royal preacher Jakob Fabricius gathered officers and sang psalms in the rout, and hundreds of soldiers stopped. I believe that the Swedish Army was effectively saved by this act. When the army learned of the King's death, they were not leaderless, as Bernhard had already taken control, but they were vengeful. "They have killed the King! Avenge the King!," was the charging cry as they headed straight at the Imperial line, taking the day.
To your question: Had Gustavus Adolphus not died, the battle probably would've ended earlier in a Swedish victory. Had the Army never learned of his death, the battle would more than likely ended in a stalemate, or close Swedish victory. Simply because the death of the King gave the Swedes inspiration to win. Wallenstein would more than likely not be able to win, in any case.
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