Except if you're Danish, students are always excluded when counting who's poor or not. Technically students are poor (mostly), but it's viewed a temporary, and therefore they're not included.
In America, only college students that live off campus and do not live with relatives are counted in the official poverty rate. I can't really see why they should be excluded, since they are living in poverty that is just often propped up by debt.
But, the census bureau also calculates an additional poverty rate that excludes college students.
It should probably only include people mid-twenties to mid-fifties or so, which should hopefully avoid most intentionally underemployed people. I care about breadwinners, not dependents.