Oh, OK. If you do use the app, then it might make a difference. Also, if you want to continue using the app, check your Sync settings. Don't make it sync notifications on intervals (1 hour is the default), turn them off. Notifications will still come through as push, but if you set an interval, every hour it's checking for notifications, even though it's receiving them in push sync as well. And again, if you have one of the buggy situations, it would drain your battery, but it would also appear very high in the list of battery users in your phone's report.
You can try it for a couple days and compare. Disable them, use Facebook through the webpage, and compare your battery life before and after. As long as your usage remains similar, I don't expect you to see much difference, but sometimes a few minutes of extra battery CAN make a difference.