Hello, @StephC
Welcome to the DocuSign Community!
Yes, each individual Admin user takes a seat.
As Best Practices, DocuSign recommends at least two Admin users in the account. When an Admin is out of office or something like that, the another one can act.
There is also another way to permit a Sender User to do Admin tasks, as for example, manage users. You mentioned that your Admins only Add/remove (close) users.
You can customize a Permission Profile (copy the DS Sender profile, give a new name) giving some Admin permissions, for example: manage users. After the creation of the customized Permission Profile you can assign users to that new profile.
To learn more about Delegated Permission, read this article. You can download a Best Practices guide for Delegated Admin permissions.
Delegated Administration is available only for certain plans. If you do not see the functionality described in this guide, check with DocuSign customer support to determine if it can be enabled for your account.
I hope that helps!
Alexandre