Is there a setting on this board that will allow user to time out after a period of inactivity?
You mean logout? Yup, your cookie will expire.
UserCP -> Edit Options -> Login, Cookies and Privacy -> Remember my login details for future visits.
It doesn't make you log-out after a certain time per-se, instead it just doesn't remember you after you end your session (normally that's when you close your web-browser).