If the Assembly Plugin is run during the package phase, do my assemblies get deployed during the deploy phase?

Yes. The assemblies created by the Assembly Plugin is attached to your project so it gets deployed too.

Can I use an artifact created by the assembly plugin as a dependency?

Yes. You can refer to it using the id of the assembly as the dependency classifier.

How do I use the Assembly Plugin to package my project's javadoc files?

The Javadoc Plugin can generate the javadoc files of your projects. Also, the Javadoc Plugin can package them!