should the employee print business cards on his own without telling
The fact that you include the phrase "without telling his company/boss" leads me to suspect you already know this isn't a good idea.
You do not have the right to print and disburse business cards that would lead the recipient to believe you are representing your company, without gaining their permission first.
You could instead produce personal cards, leaving off all aspects of your company affiliation, if you choose. Omit the company name, address, phone number, email, logo, etc. You could include your title, website URL, personal email and home phone number.
Then you could hand those personal cards out whenever you desire (such as at a networking event or professional society meeting), without asking your company for permission - not on company time, or on the company premises, of course.
If you really want to know if your company would let you do something - ask them first!