This post is written to make clear matters of region-lock.
PlayStation 3 is region free - it doesn't mater where you bought the console, or where you buy your games, they will all be compatible. However, DLC is region-locked - for example, when you have Japanese release of game you will not be able to download DLC from your not-Asian account.
So, if you want to import JP release of Chronophantasma and you want DLC, you have to create Asian account.
I don't know if my information is 100% correct, but if something is not right, let me know it here and I'll change my post.
No, you're correct. I went through that exact series of events when I first got my hands on the Asian version of Chronophantasma. The only thing is that there is a very small number of games (only one I can think of being Persona 4: Arena) that are region-locked and won't work on a non-Japanese console.
Fortunately, BlazBlue doesn't have region-locking on any of its games so far, so let's hope it stays that way.