I can really see the desire to use one system for all sorts of different genre, I'm just having trouble wrapping my head around a 20th level investigator ala CoC. Part of the charm of CoC to me was always the relative powerlessness of the PCs. Beyond that they don't even really follow much of an upwards power curve. In fact its more the opposite. Its true that a CoC character can gain points in various skills, but overall throughout a campaign the PCs actually get weaker in the most important way (sanity) and at best get a little more competent at mundane things. It really focuses the game on plot and atmosphere since there is essentially no aspect of "power gaming" involved. Plus the investigators are always basically normal people.
In any case, I'm not saying an interesting game couldn't be put together, but I think it would feel a lot more like Comic Book Heroes vs Cthulhu than what you get in CoC. Also I do think you'd have to heavily revise the classes. 4e style fighters for instance aren't going to be terribly useful. They have really limited potential for useful skills, their melee combat oriented class features are not much use in a setting where combat is infrequent and usually involves guns and other ranged weapons, etc. Rogues are in better shape as they could apply a lot of their powers to firearms (reflavored bows etc maybe) and light weapons fit better into the genre than big two handers or sword and board style meleers. Warlord seems to me it doesn't really work all that well at all though. Some of the warlord's leader type abilities are OK, but again its too much focused on melee weapons.
Overall I think you'd have to devise some suitable classes, which is a lot of work. It could be done, but then the question is whether or not its really worth the effort and if the game is still similar enough to 4e that there's much advantage to doing it.
Granted its not 4e and the players would have to learn a different system to play CoC, but to be honest CoC is a REALLY good system. Its also a very simple system to learn, probably an order of magnitude simpler than 4e. Anyone familiar with 4e should be able to pick up CoC in about an hour of play, tops. Also consider the sheer volume of existing CoC material thats out there. The adventures are consistently very high quality and there are a number of good source books (dreamlands, gaslight, modern, etc). Anyway, maybe this is going too far off topic and I'm happy to give any pointers I can on how to do a 4e mythos game if that's what you're set on doing. Just be advised its probably a lot of work and IMHO CoC will do a better job in the long run.