No. I don't really see a reason to do it. If my body indicates that it needs something I'm going to do what my body is telling me. If that means having and orgasm, then great.
I think that for most people there really isn't much of a benefit, but for people who feel the need to or want to do it then it can be a useful exercise in discipline, but that's about it.
If I ever did feel the need to deny myself orgasms for an extended period of time to exercise discipline then I guess I would try to do it, but it wouldn't be just because it happens to be a certain month and there is a trend of not doing so in that month. I would just do it when it feels right for me.
I think its fun that no nut November cam out of Movember. Movember was started to raise awareness of prostate cancer. There are theories that frequent ejaculation, about 30 ejaculations per month, can reduce the chances of prostate (I'm not sure all the research is completed here, and the medical truth isn't really the point, it has more to do with the motivation behind the trend). It seems weird that another trend claimed the same month for a behavior, not ejaculating, which could have the opposite effect on prostate cancer.
So far I have cum twice in November after 5-6 total hours of masturbation. That is roughly the average number of ejaculations in a two day time period for me, but the amount of time spent masturbating far exceeds my average, and I'm very glad I did it.