If you are using outlook its quite easy to do it this way (just use their rules wizard for the rules):
You will need a running PC with outlook running as the target recipient (A slave PC I suppose you could call it).
In outlook on that PC go to File/Print
In the box that comes up check the box that says "Print attached files" - save that.
Set up a rule to print any new mail and maybe move to another folder/delete whatever
Now if you mail that user name it should just print - you will get the email printing though as well as the attachments.
To stop spam you could perhaps always check for some sort of text in the mail or subject heading...