I've known 2 instances of people cycling there.
1. A couple I met on a campsite in RIga in, I think, 2014. They had ridden from Poland via Kaliningrad. They had applied for visas to cycle through, and had been told that their visas would be waiting for them at the border. They duly arrived at the border, and presented their documents to the Polish officials. They explained their lack of a Russian visa, at which the Pole laughed and waved them through with a "See you in an hour or so!". Of course the Russian officials didn't know anything about a visa waiting for them. After phone calls to HQ and several hours' wait, someone was sent on a bus to the border with their documents and they could proceed. The rest of their experiences were in a similar vein, and the cycling was so unpleasant they gave up and got a train to Lithuania.
2. Mark Brayne. Former Reuters (Moscow) and BBC diplomatic correspondent (Beijing, Berlin, Vienna) who retrained as a psychotherapist. I met him on a bike path somewhere between Paris and Mortagne in about 2010, and it turned out we (and Brymbo otp) had had the same address in Leipzig in the 1970s, though several years apart. He claims to be the only person (apart from his stoker) to have ridden a tandem through Checkpoint Charlie, and rode through the GDR from West Berlin to West Germany in a single day on the transit route when he discovered there was nothing in the 4-power regulations to stop cycling it. Anyway, subsequent to our meeting I read about his 2017 tandem travels in Kaliningrad (as part of a Baltic tour)
on his blog. I've just had a fascinating re-read - as a former BBC foreign correspondent he knows how to observe and write.
[BTW I didn't recognise his voice when we met, but it sounded very familiar when I heard him on an archived <i>From our own Correspondent</i> broadcast from Beijing.
Given my difficulty (a hiccup really) getting into Russia in 2013 and a brush with officialdom while there, I wouldn't fancy it now. But then again, that's probably what they told Mark Brayne when he rode from Berlin to West Berlin.