I would say no, because a PC who is dropped to 0 hitpoints is not killed, but unconscious and dying. The Players Handbook takes some pains to distinguish this.
Death Saving Throws
If damage reduces you to 0 hit points and fails to kill you, you fall Unconscious (see Conditions ). This unconsciousness ends if you regain any hit points.
That itself is pretty-clear: If an attack drops you to 0 hitpoints but doesn't exceed your hitpoint maximum, by RAW it fails to kill you.
For example, let's say Mac the Level 5 Fighter (with a Con modifier of +2) is fighting with some Bandits. He's taken a bunch of hits, so he's only at 5 hitpoints out of his 44 maximum.
One Bandit comes up and and attacks him with its Longsword and beats Mac's AC, dealing 1d8 of damage.The Bandit rolls a 3 on the attack roll and adds a +2 mod for Strength, dealing 5 points of damage. This drops Mac to 0 Hitpoints, and he flops unconscious into the dust.
But Mac isn't dead yet. He's bleeding and dying, but he's "only Mostly Dead." This is why his Party's cleric can use Spare the Dying on him after the party defeats the Bandits in the next turn. But he will die if he keeps sitting there. And that's what the Death Saves represent.
When Mac falls to the ground, he is bleeding. He is not being stabbed repeatedly by a longsword every turn, he is only bleeding. As he lies there, some of his cuts may begin to clot, some of his internal bleeding may subside, and his overall bleeding may slow. This is what a Death Save represents. He also may pull himself out of unconsciousness and crawl away. This is what a Natural 20 on the Death Saving Throw (immediately regain one hitpoint) represents.
Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.
Let's say there's another case, a few miles away. Rosie the Rogue is walking near a mountain when a Stone Giant takes noticed. Rosie is a level 3 Rogue with a Con Mod of +0, meaning she has 18 Hitpoints. The Stone Giant throws a rock, which crashes into her, dealing a whopping 37 points of damage (rolling 4d10+6). This drops Rosie to 0, but the remaining damage is 19 HP, or exceeding Rosie's max hitpoints, meaning the Rock flattens her and kills her instantly.
If Mac dies, it's not a longsword attack that finishes him-off, it's the bleeding it caused. But when Rosie dies, it is the Rock that kills her directly. And, while this may seem like a silly distinction, it gets important when the effects of spells are added to the mix.
Finger of Death
You send negative energy coursing through a creature that you can see within range, causing it searing pain. The target must make a Constitution saving throw. It takes 7d8+30 necrotic damage on a failed save, or half as much damage on a successful one.
A humanoid killed by this spell rises at the start of your next turn as a Zombie that is permanently under your Command, following your verbal orders to the best of its ability.
So, let's look at Mac again. Mac, after the Cleric revived him and completing a Long Rest, decides to go bully a high-level Warlock NPC.
The Warlock, not amused at all, casts Finger of Death on Mac, who fails his saving throw and takes 67 (rolling 7d8+30) points of damage. This once again is enough to send him from 44 to 0, but the damage remaining is 23, which doesn't exceed 44. Therefore, Mac does not die; by RAW, the spell fails to kill him outright, but he is now unconscious once again.
Now, Finger of Death, an Instantaneous-Duration Spell, works by arcing negative energy through the target. After the spell is over, the negative energy (the same kind of energy which, by D&D official Lore, animates Undead) is no longer coursing through Mac's body. In fact, it has pretty-much dissipated after draining most of his energy.
If Mac were to fail his next 3 saving throws, it wouldn't be the spell that killed him: the magic is over and done with. Instead, it is the fact that he can no longer procure enough life energy to continue to beat his heart or breathe which kills him.
That is why Mac would not come back as a Zombie, because there is no negative energy left from the spell to animate him, that expired several turns ago when the spell's duration (Instantaneous) wore-off.