Am I hurting my chances since I am not submitting letter of recommendations?

I really have not connected with any of my professors on a personal level except for one whom offered me a position in the school’s Budget office…

If I do not submit a letter of rec when the school says they are not required, am I in reality hurting my chances?

Probably not as they do not require them

I don’t think anyone here knows for sure. I don’t either.
Personally, I like to think that it won’t hurt you, but it could be the piece of information that gets you accepted.