Can I travel to Hainan with business visa F if I'm already in China?

Hi, I hold a business visa and came for project cooperatoin with chinese company; I'm going to have one week off in August and would like to go to Hainan. Can I just go there as a traveler with F visa? I'm in China already.
Can I board domestic flight to Hainan and if yes, how will my documents be checked.

Thanks in advance.