can i travel with an f visa after my unpaid internship?

I am going to China for a 3 month unpaid internship, and my company recommanded I apply for an F visa, provided they would give me an invitation letter. I plan to travel around China for a bit after my internship is over, but that means the company won't include the date I'm leaving the country, since I will have finished interning by then. Should I ask them to include this duration in the invitation letter, or is it enough to ask for a visa that lasts longer, even though I have no justification for it?