According to Brooklyn Nets owner Mikhail Prokhorov's LiveJournal account, Prokhorov will not be participating in the ALS Ice Bucket Challenge in any public way, but hinted with a quote from the Bible's book of Matthew that he'd be charitable in a "don't-kiss-and-tell" way.
Prokhorov was nominated by Russian political activist Vladimir Zhirinovsky. Prokhorov responded on his LiveJournal account in Russian. According to a rough Google Translate, Prokhorov wanted to remind Zhirinovnsky of scripture, particularly the book of Matthew, Chapter 6, verses 2-4.
Here's the translation from the New International Version of those passages:
So when you give to the needy, do not announce it with trumpets, as the hypocrites do in the synagogues and on the streets, to be honored by others. Truly I tell you, they have received their reward in full. But when you give to the needy, do not let your left hand know what your right hand is doing, so that your giving may be in secret. Then your Father, who sees what is done in secret, will reward you.
So it looks like we won't see Mikhail Prokhorov dump a bucket of ice water on his body. Too bad. To make up for that loss, you can watch other Nets like Jarrett Jack, Billy King, and Brett Yormark take part.