No, he was not.

First, some background on Hess. He was probably the most controversial of the 'seven men of Spandau'. Conspiracy theories about him began already after his 1941 flight to Scotland, with the USSR suspecting that he had been sent by Hitler so that Germany and the UK could make peace before Operation Barbarossa began. In reality, Hess had decided to fly there on his own. His mental health had already been dubious, but in captivity, it deteriorated further until he was constantly paranoid, attempted suicide (once by jumping down the stairs and once - by trying to stab himself with a dull knife), and was driven to distraction by minor irritants such as the sound of trucks driving by the building.

As if that wasn't enough, when he was brought to Nuremberg in late 1945, it turned out that he was either suffering from amnesia or pretending to do so. Psychologists agreed that there was nothing physiologically wrong with him, but his brain had chosen this form of flight from reality as a coping strategy. However, during a hearing about his ability to stand trial, Hess suddenly insisted that his memory loss had been faked. Shortly afterward, it came back. And then disappeared again.

In the end, Hess was sentenced to life imprisonment. The Soviets called for death, but they were outvoted. From 1966, he was the prison's sole inmate - I go into more detail about why he wasn't released here. For the next twenty decades, requests to have him released became more and more humanitarian-based, as Hess became older.

Mentally, he wasn't exactly well. Several times, he seemed to lose his memory again (infuriating his fellow inmates), but he always got it back soon after. In 1959, he made another rather feeble suicide attempt. Psychologists examined him over and over and always concluded that he was perfectly capable of serving his punishment. Physically, he was healthy for his age until in 1987, he took a turn for the worse. Soon after, he was found dead, having strangled himself on a lamp cord in a little shed in the prison yard where he had sat and read newspapers.

On the surface - nothing strange about a lonely and increasingly infirm nonagenarian killing himself. However, rumours that he had been murdered by his captors immediately proceeded to race around the globe, spread by Hess' family, who had never made peace with his imprisonment. His wife and son were dedicated Nazis.

Many people pointed to the seeming impossibility of a person who could barely dress independently managing to hang himself, but one of Spandau's wardens later wrote, quoting a military doctor:

For a 93-year-old person with severe sclerosis of the brain, a minor squeezing of the neck and fear would have been enough to cause asphyxia and heart stoppage. [translation mine]

So that even if the loop did not constrict his neck tightly, it would have been enough to kill him. I am far from an expert on this, so if someone can comment about similar deaths, that would be much appreciated.

There were theories that Gorbachev was coming around to the idea of releasing him, and someone or other was afraid of the secrets he would tell, but anyone who says that forgets how much Hess managed to correspond with the outside world while in prison. Several people ended up fired from the prison for acting as his couriers. Had he wanted to reveal some sort of secrets (or, indeed, had any to reveal), he'd have done so by means of the medical orderly, or the pastor, or someone else. Eugene Bird, who was the US director of the prison for a while, made a whole bunch of secret interviews with him, with no sign of any secrets important people would be willing to kill to protect.

So it seems that the simplest explanation is the most plausible one. His hopes of release dashed once too many times, Hess made another one of his feeble suicide attempts, and this time, it was enough to kill him.

Sources:

For anything about Spandau Prison, Tales from Spandau by Norman Goda is the best you'll get. It's available on archive.org.

Tajna smerti Rudolfa Gessa [The secret of the death of Rudolf Hess] by Andrej Plotnikov is the diary/memoir of a Soviet warden who worked in the prison from 1985-87. Unfortunately, it's only available in Russian.

The Nuremberg Trial by Ann and John Tusa is rather dated but still a good source.

Serious historians generally agree that there was no great conspiracy around Hess' flight to Scotland. An example would be Richard Evans' Third Reich trilogy, which also contains quite a bit of material about Hess himself.