Your wife will log into Facebook with her email address but that is not the same as accessing via emails. You can chat between friends on Facebook (online) not emails. Any chat message doesn't use your email account or email servers and therefore will not clog it up. It is however possible that if you have a low broadband speed and both are using it at the same time, especially wirelessly, then it could slowness and time outs.
Facebook requests ie request to be a friend should only be accepted from people you know and are willing to exchange information with. You can set posts on facebook to friends only.