To answer your question directly the Achaemenid Empire was not "rotten", but there were certainly mitigating factors that made Alexander's conquest easier than it might otherwise have been. Some of that is a consequence of when he invaded and some of it is a consequence of the nature of the Achaemenid Empire.

To start with the Empire was in a bit of turmoil and palace intrigue in the immediate years preceding Alexander's invasion in 334 B.C. Artaxerxes III was poisoned by his vizier Bagoas after he had fallen out of favor with the old king and proceeded to elevate his youngest son Arses who became Artaxerxes IV to the throne. After Artaxerxes IV began chafing under the shackles of Bagoas he too was poisoned and Bagoas elevated Artashata a nephew of Artaxerxes to the throne, that man took the name Darius and became Darius III. Shortly after Bagoas tried to poison Darius as well, but Darius was successfully alerted and forced Bagoas to drink the poison meant for him. The conclusion of all this intrigue left the Achaemenid Empire in a state of turmoil. In the span of 2 years the throne had changed hands three times. Darius was in his early 40s when he came to the throne and had neither the skill nor ambition to manage such a massive empire even had it not immediately faced a serious crisis. Surrounded by malcontent satraps and disaffected subjects like Khabash in the recently reconquered Egypt he lacked the experience or personality to pull his disparate empire together. This was the state of rule in the Achaemenid Empire at the time of Alexander's invasion in 334.

There is another substantial problem that I alluded to as well and that is the makeup of the Achaemenid Empire. While there is a heartland and loyal cadre of citizenry to draw from it was also comprised of disparate and subjugated peoples many of whom were only too happy to defect to Alexander's side under the threat of conquest. Indeed the tax burdens placed on the provinces and the promise of something better under Alexander's rule made them at times very willing and capable allies.

A third reason that Alexander succeeded is that his initial invasion was not taken seriously by Darius. Indeed there was precedent for Greek invasions of Asia Minor which the Persians usually defeated by bogging them down in Asia Minor and then paying off their enemies in Greece to force their army back home to defend the city. Darius employed a similar tactic inciting the Spartans to revolt, but they were defeated at Megalopolis. Darius also presumed that his satraps could handle Alexander's invasion and saw no need to bring the full weight of the royal army to bear immediately. Whether Darius immediate intervention and action could have changed the tide is speculative, but the year between Alexander's invasion and his personal intervention did nothing to impede Alexander's success.

TL;DR The Achaemenid Empire was not rotten, but certainly was in decline, whether they could have arrested or reversed that decline is rendered moot by Alexander's subsequent and successful invasion.