Immigration status question for someone about to marry vs staying in school

I am about to marry a Vietnamese male. we will marry within a few weeks, and then start green card petition. it is bona fide. the question is this: he is an international student, his student visa expires late august. He has been in the USA nearly one full year. Does he need to be enrolled in school while waiting for adjustment of status to occur? he no longer wants to be in school. he wants to get married, get his green card and then start working. I have been told that not enrolling could put him into a less than legal status. Thanks!