Spawning threads in a JSF managed bean for scheduled tasks using a timer

I would like to know if it's ok to use Timer inside application scoped beans.

Example, lets say that I want to create a timer task that sends out a bunch of emails to every registered member one time per day. I'm trying to use as much JSF as possible and I would like to know if this is acceptable (it sounders a bit weird, I know).

Until now I have used all of the above inside a ServletContextListener. (I don't want to use any application server or cron job and I want to keep the above things inside my web app.)

Is there a smart JSF way of doing this or should I stick with the old pattern?