Normal is such a subjective term. Mine exhibits a bit of the aforementioned noise when cold as well as some chatter at slow speed such as parking lots, driveways and garages, especially when cold with the rpm's just off idle. So did my last 2 or 3 manual sports cars, especially the ones with dual mass flywheels. Whether it's normal or not can only be determined by someone with experience driving multiple manual C7's or a driveline engineer from GM. For my car this is normal. Is it normal for the C7, I have no idea but it's working exactly as it did when i picked it up at the factory with 3 miles on it and it was cleared by QC which leads me to believe it is normal.
CORRECTION - I just re-read the OP and I do not have any noise or chatter at speed, only at slow parking lot speeds and only when I'm being lazy on the throttle.