Without access to the XenForo code you wouldn't be able to test the code that you're writing or verify that you're integrating it in the correct way, or be able to use the various developer tools built in to the code base to make a valid add-on. It'll be like writing code with an arm tied behind your back while wearing a blindfold.
Not really recommended.
Additionally, you cannot have access to the code unless you are licensed or the licensed person gives you access to the code.
In short: one of you needs to own a license and have access to the code otherwise writing an add-on that extends the code isn't really viable.