Yes, Turkcell have iphone deals and yes you can bring a British mobile phone to Turkey and register it. UK iphones will generally be locked to the network that supplied it if bought on a contract. You can of course unlock it but it makes updating a bit of an art form. You can buy new iphones officially unlocked in the UK so they can accept any sim, but that is an expensive option.
There is a limit for getting UK phones registered in Turkey but I can't remember how long it is.