They're as predictable as any other hash. The algorithm used to generate the hash is known, so in that sense they're entirely predictable. But you have to run the hashing algorithm to 'predict' them.
It would be possible to put a confirmation step in the client before sending a transaction: "this transaction with have hash xxxxxx: [send] [cancel]. Since the coins used in a transaction are randomly selected by the client, you may well be able to get a hash beginning with the required byte if you have enough private keys with funds on them, and enough patience. Or the process could be automated.