The reason I asked about what turns are normally detectable is that sometimes (particularly on departure) a turn of 2 or 3 degrees for a mile or so may be really handy for dodging a cloud.
I would only turn without asking if it was necessary to ensure the safety of the aircraft.
Having said that, you are expected to fly the aircraft +/- 5 degrees of the required heading so being 2 or 3 degrees from your chosen heading is not unusual for a time.
However, these days you have to fly the departure as accurately as possible not just for safety but to ensure that the noise to cash generating machines dotted round under the departure don't send your company a bill.
Regards,
DFC