Can you use Naganadel & Guzzlord GX's "Violent Appetite" Ability to discard a Pokemon if Naganadel & Guzzlord GX is not damaged?
Yes, you can. The main effect of this Ability is to discard a Pokemon from your hand.
Source: TPCi Rules Team (2020-02-27)

Relevant cards

Note: All applicable cards may not be listed below.
SM12_158
SM12_158
SM12_223
SM12_223
SM12_224
SM12_224
SM12_260
SM12_260