I could be naive, but I'd like to think we don't.
If I were Google, I'd expect links to charity websites to
(a) occur in footers
(b) be sitewide too
(c) come from non-related websites of all types and any subject.
I also think that there will be many people adding links like you are thinking of doing right now, across the web. I'd expect Google to be able to spot the 'viral' and random nature of this.
I could be wrong :)
But a search engine worth its salt with a data set as big as theirs it should be able to tell, surely?