No. I believe his opium addiction, and subsequent withdrawal are a more likely explanation.
Although I dispise the 'trust me' type anecdotal, I can say, as one who had cervical spine surgery on Jan 17 2014, and had metal plates and screws put in my body, that coming off opium based pain medication will drive you crazy. Especially so, in one's inability to achieve paradoxical sleep.
Ridiculous. As a person who went through opiate withdrawals many times, I can say that opiate withdrawal would make a person far too sick to even get out of bed. Sickert wouldn't have had the physical ability to pull off these crimes if he was detoxing off of opiates. He would have been in his bed sweating, shaking, vomiting, and crapping his pants.