Sure but he may then decide that isn't enough.  Could take you with him until someone comes up with enough money.  Use your phone and send some messages through Tor to all your family and friends saying that when 10,000 BTC are transferred into Address xyz you will be free to go.   If the funds aren't there in 72 hours don't bother because you will never be going anywhere ever again.  No need for kidnapper to arrange for a payment drop the network would take care of that for him.   He can track in realtime the progress. 

A smart thief would have the private key memorized or have it created from a deterministic wallet.  If he somehow did get caught after money was transferred you can never prove he knows the private key, perfect plausible deniability.  When he gets out of jail the ransom money will be waiting for him as soon as he reconstructs the wallet.

The idea that technology will solve all crime is laughable.