Your Google for Nonprofit membership account allows you to control the management of your Google for nonprofits application and enrollments for all your Google for Nonprofit offerings. The account, however does not necessarily manage the individual products for which you apply once you are enrolled. In terms of which account you use to apply for Google for Nonprofits both your Gmail or your Google Apps Admin account have benefits and disadvantages. See below:
1) Gmail Address Advantage: If you use this generic gmail address for the YouTube channel, you can have multiple people manage the channel by giving out the e-mail username/password to multiple people. You probably don't want to give your Admin Google Apps account username/password out to others in your organization is my guess. Disadvantage: The downside is that if you want everything/all accounts linked to your Google for Nonprofits products (AdWords, Earth, Apps, YouTube) to be using the same Google Account, then you shouldn't go this option, you should try and make your Google Apps Admin account the owner email address for all the products you have signed up for through Google for Nonprofits, since it inevitably has to be the owner of your Google Apps account.
2) Google Apps Admin Advantage: If you have your Google Apps Admin email address own your YouTube channel then you are allowing for the potential to have all your Google for Nonprofits products linked to the same account - the Google Apps Admin one. Nonprofits often find it easiest to have one email address used to log in to any of their benefits. Disadvantage: if you make your YouTube channel owned by Google Apps Admin email address then you most likely will have to have that person only monitor the channel page as there is no multiple admin privileges for YouTube channels. Unless you feel comfortable giving the username/password out to others. Only the owner of the Google Account that's tied to the YouTube channel can manage the page.