What licence do you hold, UK or other? And what country is the aircraft registered in?
I'm pretty sure the King Air will be ok as long as the aircraft operator is able to provide you with a confirmation that the aircraft was operated multi crew. A good friend of mine who used to fly as copilot on the King Air for BAE Systems had no problem getting his hours recognized and confirmed for his ATPL issue. I also know that Netjets used to have a King Air (on the Portuguese register) and their guys had no problem with their hours either when it came time to upgrade.
However before you spend lots of money on anything you would be really advised to contact your own country CAA for the straight answer, preferably in writing.
You should really get the J32 rating though, because it's a real man's airplane and the King Air is only for poofs
