15 hours in Beijing

Hi,

I'm a Finnish Citizen. I'm going to Auckland via Stockholm and Beijing. The flight will arrive at 9.40 am and leaves at 1 am from Beijing. The connecting flight will leave from the same terminal and I have the same airline (Air China) all the way. So I guess that I can apply for the 24 hour visa from the transit desk and leave the airport for a few hours, am I right? Do I have to get my luggage first?