Yes, in short.
But the problem is that Age of Conan does not log character changes so Conan Stats does not know exactly when it happens. So its recommended to do it this way:
1) type /logcombat off in console to disable logging
2) Change character
3) /logcombat on - Turning logging back on, this will in effect make it log to a new file.
4) Open Conan Stats, change the character name to the new name