If a source would deal 0 damage, it does not deal damage at all. That means abilities that trigger on damage being dealt won’t trigger. It also means that replacement effects that would increase the damage dealt by that source, or would have that source deal that damage to a different object or player, have no event to replace, so they have no effect.
May 3, 2019 · War of the Spark
If a spell or ability causes a card to be drawn while another spell is being cast, the drawn card is kept face down until that spell becomes cast (see rule 601.2i). While face down, it’s considered to have no characteristics. The same is true with relation to another ability being activated. If an effect allows or instructs a player to reveal the card as it’s being drawn, it’s revealed after the spell becomes cast or the ability becomes activated.
January 25, 2019 · Ravnica Allegiance
If a spell or ability causes a card to be drawn while another spell is being cast, the drawn card is kept face down until that spell becomes cast (see rule 601.2i). While face down, it's considered to have no characteristics. The same is true with relation to another ability being activated. If an effect allows or instructs a player to reveal the card as it's being drawn, it's revealed after the spell becomes cast or the ability becomes activated.
April 8, 2016 · Shadows over Innistrad
If a spell or ability causes a card to be drawn while another spell is being cast, the drawn card is kept face down until that spell becomes cast (see rule 601.2i). While face down, it’s considered to have no characteristics. The same is true with relation to another ability being activated. If an effect allows or instructs a player to reveal the card as it’s being drawn, it’s revealed after the spell becomes cast or the ability becomes activated.