Quorum reads + writes and applying non-destructive updates only are enough to get linearizabile consistency in Cassandra, even if clocks are not perfectly synchronized.
If you're applying non-destructive updates without quorum, you would not get monotonic read consistency, because stale reads would be possible. You could write a row, immediately read it back from another replica and find out the row is not there, because that replica didn't get it yet. You'd have only eventual consistency.
