If your servlets are well written, they should already not have any business logic inside, but just pure request / response / preprocessing / postprocessing logic. Business logic should already be hosted in stand-alone javabean-like domain / model classes. Database logic should already be placed in standalone DAO classes. Etc. You can just use them all in JSF.
, , JSF ( API- Servlet - ) beans HttpServletRequest, beans HttpSession, beans ServletContext. , , ExternalContext#getRequestMap(), #getSessionMap() #getApplicationMap(). , .
, FacesContext Servlet Filter, . bean? , , PhaseListener?