after you file, there is about an 18 month waitlist. so as long as she keeps her student status for that time, she can stay with you and eventually adjust. Or it can be very quick if you become a citizen.
Giacomo Jacques BeharImmigration AttorneySan Diego, CACA licensed ·
Only if she maintains valid non-immigrant visa status, such as F-1 for instance, during the 24 or so months your petition on her behalf would take to become "current' and enable her to adjust status in the USA without having to depart.
As a permanent resident, you can sponsor your wife for a green card, but due to the wait list for green cards, it will take 1 1/2 to 2 years. During that time she must remain in valid status - your sponsorship will not keep her in status during that time.
And to add to the other attorneys' answers, don't forget that to qualify you must truly live as a married couple. USCIS checks, and does not look favorably on marriages which are solely for immigration purposes.