From the FAQ
Q) Do I have to pay you a fee for the code?
A) As long as you don’t make any money off the code, you don’t have to pay us anything.
Q) Can I host a game on my own website?
A) Yes!
Q) What if there’s a “Donate” button on the webpage with the game?
A) That falls under the phrase “making money”.
I would suspect that the answer to your question is yes you would need to have it published by CoG.