Fostering a cat to save money

I've never fostered before, but I have been considering it because I am planning on going to grad school in a year and thought that it may be a way for me to have a cat and save money - since my understanding is that the shelter would pay for vet bills. Also, do we feel like fostering while I am in grad school is a horrible idea? My cat recently passed away and I feel so sad existing without a cat, but I am trying to consider the most responsible choice I can make.

TLDR: Would fostering save me money and would fostering during grad school be a bad idea?