I have a workflow rule set up for the Invoice module in Zoho Inventory. Once Zoho Books and Zoho Inventory are integrated and the sync is established, will the workflow also be triggered for the invoices created in Zoho Books?

No, workflows set up in Zoho Inventory will be triggered only for the invoices created from Zoho Inventory and not for the ones created in Zoho Books. A similar Workflow Rule should be configured in Zoho Books.