Fly...we are beating "your horse" to death, but YES....get notarized prior to visit or you WILL be turned away. Also, "cover up" what your paperwork is about if you are concerned. A notary simply observes you signing and that it is indeed your signature. WHAT you are signing is not and should not be their concern. In short, they could notarize a blank piece of paper.
With regards to SSN, you may as well provide to expedite the background check. They already have it, and likely forego delays.