Does Web Based Printing Make Documents More Secure?

Does Web Based Printing Make Documents More Secure?
I've been paying attention to the Google Cloud Print project at Google Code. With Google Cloud Print you can:
  • Register any printer to be accessible via the Internet for printing by authorized users
  • Allow authorized users to print to this device with multiple devices (desktop, laptop, mobile phone)
Seem like as a business owner I would be able to temporarily open up my printer for a client, vendor or customer and allow printing. Then the person printing could send a document straight to the printer without actually sharing any digital files.

Would this make documents more secure?

I could send only printed copies to someone I wanted to view my document. Since it was transmitted over the web, the document transmission could be logged showing that a single print copy license was delivered to this business at this address.

Seems like it could add a new layer to secure document sharing.