That would depend on how far into the future the People found out that they were allegedly duped.
I'm still researching Arthur, but if decades passed, the people might not be as incensed over it as they might if the president were still in office when the truth were revealed.
I'm assuming that that we didn't have www.chesterarthur1885.com during his presidency (but I could be wrong).
-PJ
Short answer: It wouldn't change the Constitution at all.
Longer answer: If it had been known when Arthur was in office, there would have been legislation and contemporaneous commentaries, which wouldn't have changed the Constitution, but would have shed some light on in how it was interpreted at the time. There would also have been litigation, which would have set some sort of precedent.
If one unqualified president slipped through undetected, it doesn't change the law, any more than one killer who isn't caught invalidates the murder statute.