Third party apps cannot run in the background. Apps in the app switcher are not running, they are in suspended state (stored in memory at their last position). They cannot request CPU time or move data.
Some can complete a single task after you exit the app, like finish downloading/uploading but they are only given I think a max of 2 minutes to do so after which the app is moved to suspended state. But this would not add additional data use as the downloading/uploading would occur anyway.
This is mostly true -- except as also mentioned that many third party apps do continue to run in the background (e.g. Streaming apps, gps trackers, VoIP apps, navigation apps), and apps may request up to ten minutes to complete downloading and uploading activities.
I believe that Facebook will continue an active upload or download if it is in the background, but it has a max of ten minutes to complete before iOS moves it to a suspended state.
For a good read on this, see here:
http://speirs.org/blog/2012/1/2/misconceptions-about-ios-multitasking.html
Also here:
http://www.imore.com/2011/02/18/tipb-answers-close-apps-multitasking-dock/
Now the source of the additional data is a good question. If you noticed a recent spike, did that increase coincide with new Facebook usage? I am inclined to look for other explanations (unless they are new users to Facebook). Did they download a new podcast app that allows downloads over 3G? Download a few podcasts and you could add a half gig of data. Are they skyping over 3G?
If their phones are jailbroken, a host of other possibilities exists (FaceTime over 3G, downloading some apps over 3G could eat up a gig just for one app). Let us know if you discover anything!