I believe that its pretty unlikely that you'd get in to the School of Nursing but not UW; however, you do need to make sure to comply with all of the guidelines outlined in your acceptance email. Make sure to apply to UW by the deadline and submit pre-reqs on time as requested. I'm in the current ABSN cohort and the application to UW was more of a formality. You already did the hard part of getting accepted to the SoN, so congrats!