This is not possible out-of-the-box and is actually quite tricky to develop, but not impossible.
I am considering adding this facility to one of my company's products (We create SharePoint PDF Conversion and manipulation software) and it will involve something like the following:
- Add a button to the SharePoint ribbon using the standard facility for doing this.
- On the server merge the files together (our software already has a facility to do this, but you could get a third party .net library for PDF merging)
- Send the resulting file back to the browser where the user can open the PDF and print it.
The disadvantage of this approach is that, when printed, it will go to the printer as a single job so you cannot control such things as automatic stapling or starting each document on an odd page (for double sided printing).