No, taking or dealing 0 damage never counts as taking or dealing damage.
If you deal 0 damage, you have not dealt damage. Dealing damage is a binary state, you either have or you have not, there is no in-between, there are no partial successes, you don't get a medal for showing up. RAW, everything is pass/fail, and there are no rules in 5e that make exceptions otherwise. When you make an attack roll, you either hit, or you miss. When you save vs a spell, you either succeed, or you fail. When you roll a skill check, you pass, or you don't. Damage is no different. From a language standpoint, "I dealt 0 damage" and "I did not deal damage" are the same statement. From a mathematic standpoint, "0" is a null value, and represents something that doesn't exist.
Consider this analogy: I hand you a check for $0.00. Have I given you any money? I gave you a check, yes. But that check is a representative of zero dollars. In other words, you didn't get any money.
Consider also: Hitting with an attack and dealing damage with it are separate events, not the same event. There are abilities that trigger on a hit, such as certain monsters that automatically grapple you when they hit with an attack. They don't care about damage dealt, they care about whether the attack has hit. Abilities that care about damage dealt don't care if an attack was a hit or miss, they only care about damage dealt.
For those that argue "there isn't a damage minimum", you are flatly incorrect. According to the Basic Rules, under Damage Rolls
With a penalty, it is possible to deal 0 damage, but never negative damage.
This means that 0 is in fact the damage minimum, because the only numbers less than 0 are negative, and by the rules, damage cannot be negative.
Further, the game does not, in any text rules or otherwise, differentiate between dealing 0 damage because you missed, or dealing 0 damage because the target was immune, or dealing 0 damage because the attacker is just really weak, or dealing 0 damage for any other reason. It doesn't differentiate, because there is no difference. Zero is always equal to Zero. Both sentences "you didn't deal any damage" and "you dealt 0 damage" are grammatically correct, and completely interchangeable. They represent the same event, that is to say, they represent that damage did not happen. The fact that one phrase was used over the other is not sufficient evidence to claim that a contradiction exists.
How do we know that this is the case though? How can we be so sure that "dealing 0 damage" is the same as "not dealing damage"?. Two reasons. The first is that There are no hidden rules. There is not a rule that exists that differentiates "not dealing damage" and "dealing 0 damage" and "dealing no damage". Secondly, when ever any word has not been given an explicit definition or rules text by the game, such as Invisibility or Stunned, the we use its Plain English meaning. And in Plain English, 0 means that there is nothing.