Yes, this would be absolutely fine to do. Colleges are often extremely sensitive in these kinds of circumstances. Personally, my father passed away a few days before my interview. They offered me a number of choices: to postpone the interview to a time I would be comfortable, to postpone my interviews to the next academic year and join the next year's cohort, or to consider my application without interviewing me and just go off my personal statement, grades and written work. Obvs I can't promise that these will be the exact options they offer you as it may depend on the college/people/department, but I can guarantee they will try their best to work around you and help you through the process. I'm so sorry you're going through this, though at the same time, I remember vividly how little the word "sorry" helps. Let me know if I can help in any way at all or if you want to reach out.