First, you should be aware that I-131 does not confer status, "Advanced Parole" is simply a document that enables an adjustee (someone with I-485 pending) to travel abroad without abandoning their application.
Having said that, you should be aware that an F visa holder applying for I-485 places the individual is a very delicate position. She is technically not supposed to be able to maintain F status because she filed I-485, but USCIS generally will not enforce anything against her as long as she maintains her F-1 program of study and does not leave the US. Your wife should be aware that, because she filed I-485, she cannot leave the US and return on an F-1 visa. In other words, although she is currently still in F-1 status, her visa in her passport is no longer useable. As she applied for I-485, that is clear intent to immigrate, which is against the purpose of an F-1 visa. If she travels abroad without an Advanced Parole document, she will be deemed to have abandoned her Adjustment of Status application AND she will probably not be admitted to the US on the F visa because she previously applied to adjust status which, as I said, is clearly intent to immigrate. So if she plans to travel, she must have advanced parole, knowing that when she returns, she will be a 'parolee' eligible to work by virtue of her EAD but will not be in F status anymore.