I imagine not, but would it be appropriate for the site to be rebranded for a month or a notice put out to promote the international Men's Health Charity movement Movember?
You could try to do it as a community promotion ad. The guidelines for a community ad on programmers are fairly open, you just have to convince enough people that it's a good idea.
I fully support the Mo-vember cause, so have some sympathy with the suggestion.
However, charity support is a very personal matter, and I would be against any in-your-face adoption of any charity by this site (or any other SE site)
So my answer to your question is a resounding No.
But I like the Community Ad idea
Based on @freiheit's suggestion, I've added a community ad you can vote for.
At the moment, the link is to my donation page, leave a comment if you think a different URL would be more aposite.