I believe there can only be one administrator per account. Basically, the one who created the account. You have access to the account. I think the only thing major thing you don't have is access to Analytics through the Adwords account but if you need it, the client can simply add you.

When you link an existing AdWords account to your My Client Center (MCC), you'll be asked to choose a level of account access: User Interface and API or API only.
User Interface and API access provides account managers with traditional access to a managed account through both the AdWords user interface and the Application Program Interface (API).

AdWords account hierarchy is very flexible and can get quite complicated and form complex structure like DAG. Multiple MCC accounts can be linked to multiple client accounts via User Interface and/or API. Linking with user interface means that administrating account can view and alter client account's data via web or some other GUI (AdWords Editor) interface. API linking provides administrating account to access client account programmatically via AdWords API.