Taking iPhone 5 to Europe - Can I Just Insert a European SIM Card?

So the iPhone 5 is GSM compatible and has a SIM card slot. So I can simply buy a prepaid SIM card from Europe (Italy for example) and put it into the iPhone, and it will work - without unlocking?

Additionally, anyone know of any reasonably priced providers in Europe. Don't need a lot of minutes and I'd like a little bit of data.

Thanks!