Not locked, but you can only choose one data center
Umm, no.

You don't choose a data center. You choose a server. There is no difference between playing on a different data center and playing on a different server

Data center1
-server1
-server2
-server3
Data center2
-server4
-server5
You don't pick the data center, you pick the server. That server is physically located at a certain data center, yes. The only difference between server 3 and server 4 is how good your ping is going to be. You can still make characters on all 5 servers, and play on any one of them at any time.

What you telling me is if I choose NA ( Which I am because I'm not dealing with lag) then I will still be able to play "with" the people that are using the Japan Data Center?
Yes. Again. you don't choose a data center. You choose a server. You are not locked out of playing on a JP server if you first picked an NA server.