Oh sure. I have several boys that completely ignore the mirror, could care less about the thing. One is even scared to death of it(granted, he'd jump out of the tank if he saw his own shadow I'm sure, but still....)!
Also, generally when you bring a betta home they're pretty young and spunky and excited, but after some time they settle in, get used to things, get a little older, and become a little more mellow......though it also largely has to do with personality; some are more mellow then others, and some are more feisty and aggressive then others.
So long as your guy is active, healthy, and eating normally then thats fairly normal. ;) Its just how he is.