Anything is possible, I think the issue with hospitals accepting BTC is that they would rather not take the risk of bitcoins price plummeting, now a good alternative to this is to have a system in place that would automatically transfer the bitcoin to FIAT once the transaction is complete. Another problem would be the high fees of bitcoin. Additionally It's nice to see as "mjglqw" mentioned, that a hospital is currently accepting bitcoin and would be great to see more hospitals follow this path.