Steve, that user of yours is quite patient giving that he had to enter CAPTCHA for sending out messages.
>>Issere a way to limit a user sending private messages until they have so many posts or whatever?
We don't have a ready solution that could have worked exactly the way you want.
As mentioned by other users you can use user roles and user credits.
Right now users can't sent more then 1 PM in 20 seconds.
So changing 20 seconds to a greater number might work for you, but this will be irritating for other members who might want to send PMs more often.