Unfortunately, I don't really think that will have much of an impact on the divorce rate. It wasn't that long ago that the state of New York had no provision at all for no-fault divorce, and even now it's still fairly limited when compared to many other states, but the divorce rate in New York wasn't any lower than the rest of the country. Essentially, eliminating no-fault divorce only forces people - who are bound and determined to split up no matter what - to invent a reason that fits within the acceptable grounds laid out by the law. E.g., back in the day, "mental cruelty", as vague as that is, was one of the most often cited reasons for divorce, and the vast majority of the time, family court judges are loathe to really question someone's reasons for wanting a divorce - she says he's mentally abusing her, and judges don't really get too far into investigating the truth of that, particularly if the divorce is uncontested. They just rubber-stamp it and move on to the next case.
Realistically, the law has made divorce very easy since the late 1800's in most places, no-fault or not - it's really not much harder to get a divorce nowadays than it was in 1890. The difference between now and then is almost purely cultural, not legal - back then, divorce was seen as something of a badge of shame, unlike today, which had the effect of making divorces rarer than today.
This is not to say that ending no-fault divorce is somehow a bad idea, just that I don't think it's a panacea by any means. The real change will have to be cultural, not legal - when divorce is frowned upon by society, divorces will decline, regardless of what the law does or doesn't say.