I suppose it depends on what you're using in CKeditor, or what you plan to use later. Personally, I'd suggest renaming the file (something like) contents.css.old and creating a new contents.css file, copy across all the styles that you think you'll need and then destruct-test your implementation of CKeditor, to assess whether you've got all the styles that you need.
Add to, or remove from, that file to get your finished version and then use that one. I'd strongly advise keeping the original version around though, for future development purposes.
To your specific questions, though:
Is contents.css required by CKeditor, or used by default?
I believe so.
Do I even need this file on my production site?
Not so far as I know, its absence will likely cause things to look a little less-pretty, though, until you apply your own styles.
As suggested, above, though, I'd rename the original and then create your own stylesheet with the same name, it's rather easier than going through all the various js files looking for, and changing as appropriate, references to contents.css.