To directly address your question, no, content scripts cannot be used on extension pages. While it is technically possible to inject scripts in an extension page, this uses a different mechanism that is not, strictly speaking, the same as the content script system.
Assuming you're planning to publish your extension to the Chrome Web Store, there are some very important caveats to what wOxxOm shared.
First, features like content scripts do not interact with other extensions. This limitation is an intentional aspect of the platform.
Second, the
API use section of the Chrome Web Store Developer Program Policies states that "Extensions must use existing Chrome APIs for their designated use case."
Third, the Debugger API should not be used as a way of working around platform limitations. If your extension's
single-purpose is not directly related to debugging websites or extensions, you probably shouldn't be using this API.
Fourth, disabling the debugger banner using the command line flag as suggested is very dangerous. Please, do not suggest that end users use this flag.
Simeon - @dotproto
Chrome Extensions DevRel