Break ups are a horrible thing to go through. That being said, there is a big difference between you being broken up with and you being the one breaking up with the other person.
Being broken up with sucks. You're depressed for a while and it fucks up your whole mindset on everything. I've experienced this before as I'm sure mostly everyone else has and it's a shitty feeling. You can't eat, can't sleep, everyone can tell that something is wrong with you because you sort of mope around for a while till you get over it. And I know people who have taken a lot longer than usual to get over a break up like almost a year if not more. So yea I can see how that could affect someones training.
But breaking up with someone isn't that bad. Example: when I broke up with my most recent ex, I was the one who decided to break up with her because I was just over our relationship, and I was fine by the next day. And the only reason I say next day is not because I was sad on the day of or anything, but I just felt kinda bad since I broke the girls heart so I had a bit of guilt on my shoulders for that one day when I let her know it was over. But that guilt didn't last for long.
In JDS's case from what I have heard him say in interviews, it sounds like he just isn't really feeling her anymore so he decided to end the marriage. So although I'm sure he feels bad about it because he just totally crushed his wife's feelings, this type of break up is not that hard to deal with when compared to something like finding out your wife cheated on you with some other man and no longer wants to be with you.
So I guess what I'm trying to say is, it could have had somewhat an affect on him, but to me it just sounds like another excuse. And personally as a fan of JDS, I kinda wish he would just take the loss, not make any excuses, and just promise everyone he will come back stronger and fare better next time like Cain did after their first bout.