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Yes, certain functions do work, and basic connectivity works through the double NAT. However nothing you've mentioned actually requires the use of your own router, all these functions are things the Superhub could have done fine on it's own.

One major issue is the idle timeout on the Superhub (for e.g. SSH connections) - which will not be solved by using your own router. Other things the Superhub doesn't do well (e.g. UPNP) can be solved using your own router without bridge mode, but not everything.