CS PhD Addmission: Contacting prof about unpublished work
As I understand your question, you did already submit your application, but didn't include the unpublished papers nor any reference to them? Because that is what I would have suggested: if you have an unpublished paper with high relevance to the field of your application, you could include it with your application documents.

In your case, since you didn't include it in the application, I wouldn't send it unsolicited to potential advisors, especially not if you didn't send your application directly to these people. Rather, you could ask the contact where you submitted your application whether you could amend it with a recently finished paper relevant to the proposed research topic. You would have good arguments if the paper was only finished after the application deadline.

I wouldn't expect too much though. If decisions are already taken, it's unlikely that they will be reconsidered. Anyway, since you mentioned the papers in your CV, I don't think it would be a major factor for your application whether they are included or not.

Note that these suggestions would only apply to unpublished work which is already submitted for consideration in a journal of conference. If it is not yet submitted, I wouldn't send it with the application nor to potential advisors.