No, though in some states that wouldn't hold up anyway, given that he readily admits that they had the sort of relationship from which they could "break up". He was stupid to do it, and she was stupid to use somebody stupid as a donor. Heck, it only costs about $300 to use a reputable bank, and get a sharp PhD or MD or JD who's been screened for a raft of diseases and genetic problems. This poor kid will probably have an IQ of about 60, given the parents' mental abilities.
Any agreement between a mother and father (read: sperm donor) that supposedly prohibits any claim of child support isn't worth the paper it's written on.
Legally, the child support belongs to the child (Yeah, I know. Hold your laughter.) The mother may not enter into an agreement to prevent said child from receiving his or her legally entitled support from a non-custodial parent.
At least, that's what the lawyer I hired told me after a friend asked me to provide sperm so she could get pregnant without a pesky husband around.