If the coaches Hud is Premium content then, yes, it would. However, any Premium stats would be re-downloaded automatically for content that you purchased/subscribed to.
If you have removed NoteCaddy from your license then that should work, although I would suggest that you rename the file instead of deleting it, just in case.
If the coaches Hud is something that was added by importing a Hud profile, then the stats from that would be stored in "StatDefinitionsCustomized.pt4" instead, so wouldn't be affected by removing the "External" file.
I would still recommend renaming the "External" file to start with instead of deleting it, until you are sure that it only removed the correct information.
If you still have NoteCaddy in the PokerTracker Apps menu then please open a
Support Ticket to request that it be removed from your license.