There was a post in the german part of the diablo forum stating that you can only open challenge rift bags that were earned WHILE THE SEASON IS ACTIVE. I'm not sure if it means you can't have the bag from this week if you do the rift prior to the season start, so I'll be waiting for thursday.
However you certainly won't be able to open last weeks bag on your season characters.
Timer on the current CR indicates it will still be active when season goes live. Considering the contents aren't that big a boost for most of us in NS, I'd wait till season start before doing the CR and earning the cache.