This is a good idea. getmonero.org could have a page on the site where people can choose to mine for a while for a certain charity. It would be a really good marketing stunt
getmonero.org should be setup to do this.
It is an amazing idea.
We could choose also some marketing active charities and inform them about it. It would improve the XMR image.
Also donations to the development fund could be done on this way.
Whilst I appreciate that the concept behind that type of mining and see the potential in micro transactions through this, then it is an entirely bad idea to do any charity-related thing through official monero sites - such as getmonero. Why? Because Monero is apolitical. No matter which charity there will always be some sort of political underpinning.
What COULD be done is to do browser mining where all proceeds went to the monero foundation address instead - one could set it up when idle, and people could choose a cpu% or such. That would make it possible for people without technical know how or motivation to donate that way.
Unrelated to the official monero sites someone with the ability to carry through could setup donation sites - with the use of monero of course.