Alchemy certainly does not have as its goal mystical experience/gnosis. It is literally just the science of producing the Philosopher's Stone, including all of the necessary prerequisites to that goal such as a sufficient understanding of nature. The fact that Khunrath places Alchemy only after medicine and before natural magic in his path towards Hermetic gnosis should serve to convince you of this point, but even just in the classical Hermetic path of Alchemy, Astrology and Magic we see that Alchemy was only the first science to be studied.
What Alchemy does, as Khunrath excellently puts it, is produce a longing for the Divine, and increase the longing of he who already has such a longing (arguably everyone who pursues the art). However, Khunrath phrased it in religious terms, saying it makes pious whoever it doesn't already find pious.
The point about piety is important to this discussion because we must remember that Alchemy cannot be discovered without piety of some sort. Prayer, meditation and other acts of religious devotion are indispensable in the Hermetic path (as well as any other spiritual path). So rather than leading to the end of the goal, Alchemy can be seen as an initiation, nothing more. It initiates the neophyte into piety. It shows him (granted, only if he succeeds) that only by being pious did he succeed. This is why the true alchemists cry the praises of hallowed piety in their books: they know that without piety, they would not have succeeded.
Consider how the sciences which Khunrath mentions before Alchemy - natural philosophy and medicine, respectively - do not require any form of piety to learn and practice well. Consider how the sciences he places after Alchemy - magic, kabbala and theosophy - all require spiritual knowledge. Alchemy falls somewhere in between, neither requiring spiritual knowledge (it is entirely rational) nor being possible entirely without any kind of spirituality - the latter being the case since in order to discover this art, one needs to think along the lines that nature works; and this is only possible if one's mind is in harmony with nature. This in turn can only be possible if one's mind is illuminated by true wisdom, which, again, is only possible through some form of spiritual practice.
It is true that if Alchemy were written about openly, anyone would be able to learn it. It would not require any kind of spiritual ability. An adept could probably teach it to an atheist Aristotelian natural philosopher through plant morphogenesis - a process which is visible, contains all of the required materials, and doesn't require a belief in the heavenly realms (although admittedly, he would probably have a hard time explaining the "dot" of the philosopher's, contained in the matter, without which the art is impossible). What distinguishes Alchemy is that it has to be discovered independently by the student. Nothing works for this other than sitting at the feet of nature through practical experiment - the books are only a guide to this. And nothing can make learning from nature successful - especially when nature speaks in its own kind of code language, not openly revealing its secrets (although as every alchemist claims, its method of teaching is still much clearer than their books!) - except if there is some kind of harmony between student and teacher. Which of course brings us back to what was mentioned above.