Is there any way to adjust his status if I marry him, or would be barred as soon as he leaves the country?

When a U.S. Citizen marries a foreign national who initially entered the U.S. lawfully and with inspection, but then overstayed his visa, the couple can complete an Adjustment of Status application process in the U.S. in the Immediate Relative visa category. The fact that the fianc? overstayed his visa (or even worked without authorization) will not bar eligibility for adjustment of status to become a Lawful Permanent Resident (to get a "Green Card"). If the husband temporarily will be living in another state in order to attend college, the process will become significantly more complex, since the couple will need to persuade a skeptical USCIS adjudicating officer that the couple should be deemed to be living together in a bona fide marriage notwithstanding the spouses staying in separate states. This can be accomplished with extensive documentation demonstrating the bona fide nature of the marriage, for example with documentary evidence showing attempts for the foreign national spouse to attend college in the state where the U.S. citizen spouse lives; showing attempts for the U.S. citizen spouse to find a job where the foreign national spouse attends college; evidence of visiting on weekends, skyping/texting/calling and similar details; evidence that the couple has "put their financial lives together," etc. Especially for a case with such complexities, it would be wise to engage an immigration attorney for representation. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.