As far as I know UW does not admit according to proposed major otherwise students would list the major most likley to get them admitted. You are admitted to the university as a whole. Some schools/colleges that otherwise do not admit freshmen currently have direct admits- engineering and business are two.
So far computer science is not a restricted major. You can easily switch majors, especially in L&S (the college that most students are in, the default college for freshmen who do not state a different one). Putting down a proposed major on applications is useful in having HS students have goals for their college education. It may also help UW plan on how many sections of various courses should be available to meet probable demand.
Therefore listing CS as a proposed major should make no difference in acceptances. There are no designated “CS spots”. CS is not a competitive major, at this time it is a popular one.
There is limited space in various engineering, teaching, nursing, business and some other fields due to facilities available (consider lab space, practical experience) or numbers that can be accommodated compared to numbers interested. These are competitive because of this.