Official response from Adriel Hampton
Yes, NationBuilder's online fundraising features and forms are NYCCFB compliant. You will want to use Authorize.net as your payment processor. We have been running New York municipal fundraising pages since 2011 and several sites have been reviewed by CFB officials.
Note that you do need to properly use the bank account settings specific to New York City - you can find those under Settings > Bank accounts. If your CFB officer has questions, connect with your organizer at NationBuilder and we can help.