No, That noise that happens at cold start is the cold start light off used to heat up the catalytic and lower cold start emissions. It's caused from the way the cam timing is requested during cold start and likely a portion of the combustion event actually going out the exhaust valves to heat up the pre-cat.
This is speculation on my part, but educated speculation based on my knowledge of emissions control systems.
I asked in a forum about it when I first got my 328i, as my sales consultant didn't inform me of this "feature", and knew that if it was normal then it was emissions related.
Once I get an OBDII reader that works for my 328i I'll record cam positions, timing and 02s to show how this process physically works.
I can't believe there aren't any BMW videos or technical briefs that explain this feature..
It's a real neat detail that HAS to have people returning their cars to the dealer for warranty issues in the fist 90 days of ownership for no reason.
There are a few SAE docs on cold start cam timing, but not any that I have seen that specifically say BMW uses it.