Hi jad,
Some customization can be done to achieve this goal. I don't think you can add the count right on the grid but you can add it elsewhere on the invoice. Add a textbox or a label object somewhere on the invoice. This will be used to display the count. Next add the following actions into your Save button. Alternatively, you can make a button that updates the count.
First use the action Retrieve value from table. You'll have to retrieve the LineOrder field from the InvoiceLine table where the InvoiceRecordID field is equal to the active recordID. Retrieve the maximum. The logic behind this is that the LineOrder field tracks the order on the invoice and the maximum number (the last item on the invoice) will be equal to the count. Make sure to then enter this action result into your desired object using the Enter Value into Field On Screen action.
When you're entering new items into an invoice you will have to Update the grid before you proceed to see the updated count.
If you need consulting help I can put you in touch with one. Just remember this is a paid service. Hope this helps!
Jason