I was considering including the source code in my archive file (EAR, JAR, WAR) so we could see what the deployed application looks like. This will obviously make the archive much bigger. Does the size of the archive file affect performance on the application server at all? Is this a good idea or not?
It does affect the performance to the extent that there are more entries in the archive's index but that won't be too bad and you'll put the source in its own subdirectory. Or you can just make a source archive and shovel it around with the other files. That would be my choice. Of course if this is a GPL distribution, you'll have to be explicit about where the source is located.
Here's another solution to your problem which can come instead (of putting the sources in the .jar) or in addition to it: Specify the source control revision id to the .jar. You can specify it in the manifest file or in a properties file.
The source control revision id is the current id associated with the root of your project on the source control system. It is readily available in SVN, Git and most modern source control systems. In older systems (CVS) you must first create a (named) tag probably by using current date and time (to ensure uniqueness). The revision number will let you to retrieve from the source control the exact snapshot from which the archive was obtained, so when you fix bugs you'll be fixing them on the correct sources.
This technique will allow you to save space - you won't need to ship the whole source directory.
However, it is still a good idea to specify this number even if the sources are included in the archive simply because it unanimously specifies the point in history where the archive was created. Manually comparing the sources in the archive with those in the source control is a pain.