I would estimate network traffic over 24hrs would avg at 32-64Kbit/s per GH so it can still add up to quite a bit of bandwidth usage on a limited plan depending on what plan you have.
I did not check my network traffic. I consider it insignificant as well. However, 64Kbit/s is not insignificant. This is 8KB/s which is 480KB/min which is 28MB/h which is 675MB/day which is 19.8GB/mo. This is like a bit over 4 DVDs per month or 1 DVD per week.
EDIT: I measured my rig:
3.54 (Kbit/s) / (GH/s) download (received)
3.34 (Kbit/s) / (GH/s) upload (transmited)