The risk is that your virus definitions will be out of date by a week. Many new threats are discovered each day and added so you need to weigh this risk. Personally, I would update every day but I'm not sure of your situation.
Since your network doesn't have Internet access, the risk can be smaller. Do you allow external device storage? If so, you may want to think about updating more frequently.
Without Internet access, is your virus count high or very low?