...does this much difference in rating signal that it is possible that one is cheating?
Nope. I'm about 1480 in regular, and an awful 650+ in Random Chess. Rating is an indicator of where you stand in the population, and some people are just really good at certain variants.
I dunno, it seems to me that some people just really suck when it comes to having to play under the pressure of time, tick-tock. Perhaps this guy is one of them and he just is good when he has time to really work through things. Also, aren't computer allowed in correspondence chess nowadays? Also, maybe the guy's got a terrible opening and the opening books are getting him through that part of the game...