How do schools typically handle a request for short-term leave from a student?
Colleges do not prohibit such events because colleges can't prohibit such events.  On the contrary, colleges have policies explicitly permitting absences for certain specific reasons: travel on university business (including athletics), documented medical emergencies, deaths in the family.  There is typically a special grade of "Incomplete" awarded if the material missed is critical, such as a final exam; the student takes the final soon upon returning and the grade is adjusted accordingly.

As for what the professors will do, this is highly variable.  Some will be accommodating and will extend deadlines, others will mark missed work with zero, while a few might even kick the student out of the course.  

Luckily, there is a simple solution for this student.  While enrolling for classes, at the very beginning of the term, he should speak to the professors involved and explain the situation.  If any professor is particularly hostile, then he should take a different course instead.  In extremely unlucky circumstances, a specific course will be essential to take that term (and no later), and the professor will be very hostile.  In this case it might end up that the student takes longer to graduate.