I've been thinking about that myself. There are a couple of posts here that mention the idea, but I'm not aware of anyone doing it yet. Seems like someone was discussing it just a few weeks ago in concert with BIAB mashing techniques for a true single vessel brewery.
As to viability, seems like it should work to me. If you put your hops in a bag (and adjust utilization) then the only thing you'd have to manage would be the cold break. Based on the 'no chill' method results that might not be too big of an issue. And you could drop the junk before pitching anyway. The only other concern I'd have is with all the boil junk that collects on the side of the BK...I'm not sure if that would be a problem or not.
I was thinking of using heat sticks to boil rather than a permanent installation. I'm not sure I trust the material of the element to be in long-term contact with my beer for that long. Likely just paranoia on my part, but a heat stick or two is an easy enough insurance policy (and no need to modify my conical!) With an insulated conical I wonder if the standard rules of thumb on the amount of juice needed to boil six gallons of wort are the same? I'd guess so, since evaporation has to be the majority of energy loss in the system.
I've considered using the 'no chill' technique of purging with CO2 after the boil and sealing it up with a bit of positive pressure until it cooled itself down. I'd still have to find a way to aerate after it cooled, however, so he 'no-chill' method might end up being more trouble than it was worth.
I say go for it and give us a report!