If there were two Marthas, of whom one wants to go to graduate school, the other to law school, the clause would be important in identifying her aspirations and the commas would be removed. Martha who wants to go to graduate school studies whenever she has a moment. But in neither case would we allow a single comma to intervene between subject and verb. The dash is used for interjections and asides. Parentheses could have performed the same function, but they would have integrated the aside more subtly into the sentence.
Dashes indicate an interruption while parentheses signal a digression.
If you use dashes in this way, make sure that the sentence makes sense without them. The dash has an useful but ironic quality in informal writing. This kind of usage should be confined to informal writing. Usually they surround some information not worthy of its own sentence, but which is worth inserting into another sentence. Too many parenthetical interruptions will disrupt the flow of your writing.