Can I give away Digital Products for Free using plug&paid?

Yes you can. Simply create a digital product with the price set to 0 and create a shopping cart or attach the product to an existing shopping cart. 

When you create a shopping cart with a free product, no payment options will be required. Create your shopping cart and your customers will be able to complete the order and access the digital file.

An invoice will be generated and a sale will be added which you can retrieve in your "Invoices" page.