Do community admin permissions override the permissions set in admin groups?

Yes, the permissions set by a community admin override any related permissions set for the user in admin groups.

Example:

If a user is given permission to post questions, links, and articles to Fuse as part of an admin group but the admin of a particular community has not given them permission to do so, that user will be unable to do so in that particular community.

Admin group permissions:

Community admin permissions: