Solution

Yes, they are generated by default however, Chargebee can be configured to not generate zero-dollar invoices (each line item being $0) using the "Hide Zero Value Line Items" option.  Just navigate to Settings > Billing LogIQ (under Billing section) > enable the "Hide Zero value Line Items" option >  hit Update Billing LogIQ.

Here's a screenshot.

Note: If credits and discounts are added to an invoice to bring the total payable amount to $0, the invoice will still be generated.