The answer to your question is NO. Apigee does NOT provide you with content that can be downloaded, installed and run locally. However, if you do want to do this, you would need to buy a licensed OPDK (On Premise Deployment Kit), and then go about setting things up.
Apigee does provide a FREE account however for you to play around with and perform most/ALL actions, including implementing policies and building developer applications. Navigate to Apigee Enterprise, create a free account and plug away.
ALL of the documentation you need can be found at the Apigee Documentation site.