If we submit an an application on day one including a specfication with handwritten notes on it, can the specification with handwritten notes be removed from PAIR, and can we prevent the specification with the handwritten notes from being published?

As the specification with handwritten notes is part of the application, it will be viewable in PAIR. An applicant can submit a preliminary amendment on the same day, day one, wherein the preliminary amendment would include a substitute specification. The substitute specification, not the specification with handwritten notes will be published. In the alternative, an applicant may submit a completely new application on the same day (day one) along with a new set of fees, wherein the new application would include a specification without the handwritten notes. The applicant would then expressly abandon the original application, including the specification containing the handwritten notes.

USPTO FAQ - Questions and Answers (2007JUN01)