Substituting Chicken Broth in Split Pea Soup
See no reason why not, all you will do is add more flavour. Which is never a bad thing if you ask me. Adding the ham bone will not have any adverse effects either. The recipe you are following will not have used chicken stock/broth to either make it vegetarian or for simplicity. 

Personally any time I make soup or broth at home I will use chicken stock as a base even if its just an oxo cube. At work ill use vegetable stock to keep those non-meat-eaters happy.