This would most likely reduce the number of people who would screen themselves. I wouldn't undergo a possibly horrible medical procedure for $100,000, but I might do it to save someone's life and feel like a good person.
For further reading, look into social norms vs. market norms, especially the example of the Israeli day care: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=180117 (paywall)