Input for Sales Forecasting
If you want to estimate demand, no, you do not need to train the model with unsold items for which you have supply, since they do not affect it. Having an excess supply/capacity does not affect your customer behaviour. 

If you have supply, but no demand, it needs to be there.

However, also take into account that if you have had a demand greater than the supply at any moment, you have to do proper demand unconstraining to have a good forecast of your demand.