I would call it more of a cough sound, but a bark would work just as well, and yes, this is completely normal!
The start up noise is on a cold start only, and does go away in a few seconds.
I personally like all the sounds my car makes.
If you don't like the sound just remove the CAI and put the stock air box back on, problem solved.
Some were not aware of the difference in the sound and volume the CAI will add, and ended up removing it, but most people learn to like it.
I would suggest you give it awhile to soak in, and most likely you'll learn to love it!