An online winter mooring via CRT doesn't change CCer/ no home mooring status.
Mooring for a few months (actually more than 14 days!) in a marina or on a non-CRT mooring means you should change your mooring status declaration with CRT.
Yes, there should be a change in licence fee for this period. I suspect in practice the admin fee will cost more than any potential saving though, at least for the next couple of years until the higher surcharges kick in.
If you surrender the mooring for 6 months and declare no home mooring then you'll get an increase in your licence fee. If you still have a home mooring and go out cruising for 6 months you're not CCing!