About the only thing I could find was:
Title 18, Part 1, Chapter 71, Section 1470 (Obscenity Laws)
Sec. 1470. - Transfer of obscene material to minors
Whoever, using the mail or any facility or means of interstate or foreign commerce, knowingly transfers obscene matter to another individual who has not attained the age of 16 years, knowing that such other individual has not attained the age of 16 years, or attempts to do so, shall be fined under this title, imprisoned not more than 10 years, or both
http://www4.law.cornell.edu/uscode/18/1470.html
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There did not seem to be anything in COPA that would address this other than the necessary "passing of sexually explicit material to a minor" that would be necessary for an underage webmaster to run his business...
But what I found interesting was I did not find a definition of "minor" in any of the federal stuff I looked at.... COPA uses "minor" in it's language quite a bit... Further on, it specifies that for part of the statute it is "17 and older"... I might have missed it, but I saw no straight out definition of "minor".
I would think that programs dealing with the webmaster might have some problems especially if they know he is 16... They could be on shaky legal ground because of communications they pass to him etc... But, if they truly do not know the person is underage, if they have been presented false bonafides, then they are probably in the clear too....