If I buy an unlocked iPhone 5s from the UK or USA, will it work normally in South Africa?

I want to buy an iPhone 5s but it hasnt come out in South Africa yet and when it does, it'll cost a fortune so i went online and saw that an unlocked iPhone 5s is actually cheaper overseas (eg. With T-mobile) than it will be when it gets here. Now I really want to buy it but I was wondering if it work like a normal South African store bought phone will? Will i have access to everything like phoning, texting and internet with my south afican Sim Card?