I wasn't aware there was any connection as we have been using NWE for about 7 months now. We deleted our Classic instance (whatever that means on a technical level) about 4 or 5 months ago and have seen no adverse effect regarding Proof.
@Jonathan Chen‚ It would be nice to get a confirmation from a WF engineer or consultant though.
Thanks for your responses. I submitted a support ticket about this and received the following response:
With the expiration of Classic and the fact that you are on Proof only, you don't have to worry about anything. This change only affects those on Workfront and Workfront integrated with Proof. With standalone, there are no changes at this time.
Note that my company subscribes to Proof only. I hope this helps others in the same boat who were concerned when they received the pop-up that announced the end of Classic last week when they logged into PHQ.