Are logs any use in a no logging database?

We do not use logging on our database. 1. We perform level 0,1 archives, but we don't backup the logs, do we really need to? 2. What are the logs used for in a no logging database? For example, if I update every row in a table with 10 million rows with a single update statement and I interrupted it half way through would the first 5 million updates be rolled back? Would it use the logs for this purpose? Thanks in advance.