Interesting question.
Its possible, but you should also consider that fact that many students may be deterred from going to grad school during an economic slump because its basically just throwing out money, since students dont reap the benefits of furthering education until several years down the line. I think alot of people will address their more urgent economic needs first.
The people who werent would be less competition.
The people who werent would try to save their money so there would try to save their money so there would be easier if you were rich because all the people who werent would try to save their money so there would be less competition.