Yes, to be more specific you’ll be paying for a triple dorm the first year (about $17K total), after that you have about a 50/50 chance of an on-campus apartment (where a triple room would run $4200/quarter plus food so about $15-16K per year). The lottery is independent each year, once you are off campus you can’t come back. Only once you are off campus do you need the higher budget, likely about $21K for a double for the year if you don’t stay all summer (so food is less then).
Do make sure that the comparisons with Oregon schools include differences in things like travel and insurance (will your current insurance cover OOS? Presumably it would be fine in Santa Cruz).