The goals of certain late-medieval alchemists were nonsense, but science and engineering often follow nonsensical goals (insert your favorite politically-funded project here). The major advances are usually serendipitous, and only a tangential relationship to the goals.

Alchemy had a long history, though, and often resembled practical chemistry much closely than it did a quest for chimerical substances. The practical side of alchemy produced some worthwhile facts and techniques, and overlapped in many places with early chemistry. Some late practitioners of alchemy are also honored as important early scientists: Isaac Newton, Roger Bacon, and Tycho Brahe among them. The http://en.wikipedia.org/wiki/Timeline_of_chemistry shows quite a bit of overlap.

But alchemy had to be rejected in order for modern science to emerge. There were several reasons: first, it was illegal to practice alchemy in many areas. Partly because of this, alchemists were secretive, while science advances by sharing information. Finally, Francis Bacon's work on the scientific method came along late in the game. So the only logical way forward was to re-brand the sensible parts of alchemy as natural philosophy or natural science, and proceed from there.