Upgrading jenkins using chef
So first of all, Chef is just a manner of upgrading/configuring, it will help you keep a reproducible state and keeping configuration in line but it won't do black magic and translate your jobs for you.

Now for Jenkins 1 to Jenkins 2, Jenkins-ci site says Jenkins 2 is Backward Compatible.
While this is true, when you update the pipeline plugin, not all plugins are compatible yet. There's a compatibility list on the pipeline plugin github page.

I would recommend installing a fresh Jenkins 2 and porting your jobs from Jenkins 1 to Jenkins 2. This will spot breaking plugins in Jenkins 2, allow you to strip up not needed anymore plugins and refactor your jobs.
This way you can also take advantage of defining the pipelines with a Jenkinsfile along with the code of your application.