The games will appear on the original console, until you visit the eShop or do anything online - then they'll disappear. Nintendo servers will tell the console that it doesn't own those games and they'll no longer appear on the home menu. You can get them back by using tikShop or tikDevil or similar - which will install all the tickets and allow them to be played. They'll basically be like pirated games from that point forward. You can't register them with another NNID.
Thank you again. I'll do some research on tikShop / tikDevil. Should I install those resources before making the NNID transfer?