Yes, "would" has several functions: it can be used for conditional clause, it can be used for past habits, and it can be used for "future in the past".
In this example the context makes the interpretation unambiguous. It can't be a conditional (since there is no condition explicit or implied). It can't be a past habit unless you think that joining a nunnery could be a "habit" (pun intended). So it must be "future in the past". That is from the perspective of the narrative, which is set just after the time of the "call", the act of joining the sisters of mercy is in the future. At that time you'd say "She is thirteen and she just received a call, and she will join the sisters of charity." That is the future tense. So when reporting it as a past it becomes "she would join..."
It wouldn't be wrong to say "After receiving a call she joined ..." since it is also "in the past" as well as being in the future of the past.