Maybe Peter can comment further, but my impression was that the definition of "work" is normally unrelated to whether it's paid or not, for F/J?

If those students are actually concerned about staying in status, simply saying they're volunteering might not be sufficient.

The students should speak with their DSOs (Designated School Officials) because they must have work authorization to get paid whether they're paid by a U.S. or foreign source or paid as a 1099 contractor or W-2 employee. But I don't see why both CPT and pre-completion OPT wouldn't work.