Publishing a very mediocre paper as undergraduate? Given that I am an undergraduate is it a good idea to publish a very mediocre paper (nothing novel, results way bellow state of art) in a conference/competition that accepts such papers?

Our results are good compared to everyone else (we are ranked 3rd) but the paper adds little to no value to the field and the conference/competition is mediocre (but not very bad).

Should I include myself in the authors or not, given that I am in the top of class in terms of grades and aiming for top US universities for PhD? My professor declined to be in the paper but everyone else in the team is okay with it.
So you want to publish rubbish, just to have a publication on your CV? If you really are a good student, you will find other ways to get publications. Remember that such a publication will stay with you forever, everyone googeling you will find it. On the other hand, once you have some publications, no one will care if you made your first one during your undergraduate or later.

Also: Talk to your professor. He will have reasons to decline and will be able to tell you more about the pros and cons of publishing this paper, given your academic plans. I would put quite some weight on his opinion, as he knows the paper and has lots of experience when it comes to the field, accepting or declining PhD students, etc.