I could find absolutely no evidence of an uptake of mental illness in March on either Google or Google Scholar. The absolutely only thing I can find is this: http://www.healthyplace.com/blogs/parentingchildwithmentalil... which speaks of changing seasons affecting patients with Seasonal affective disorder, well duh.
Also March Madness doesn't mean what you think it means.
The main part of the breeding season of the European hare.
Events surrounding the single-elimination Division I college basketball tournaments performed each spring in the United States. The main tournaments involved are the NCAA Men's Division I Basketball Championship and the NCAA Women's Division I Basketball Championship. The tournaments' nickname, "March Madness", originated in the 20th century and was later adopted by the media.
NCAA Basketball series (formerly March Madness series), an EA Sports college basketball video game series.
Mega March Madness, a defunct pay-per-view television package covering the college basketball tournament.
Illinois High School Boys Basketball Championship, a single elimination high school basketball tournament.
The month of the government of Canada's fiscal year end (March 31), when departments traditionally rush to spend the remainder of their budgets in order that they not experience budget reductions the next year. This usage was apparently the origin of the uses for basketball.[1]