No, critical hits must be linked with attack rolls.
I checked with Jeremy Crawford on Twitter and he says that critical hits must come from attack rolls:
@JeremeyECrawford No, since only attack rolls can score critical hits.
In response to @Kevinaskevin Can my Rogue's Assassinate cause my Wand of Magic Missile to crit against surprised creatures?
You should read the full conversation between he and I to get more detail.
Critical hits come up in the PHB on pgs. 194 & 196. As I see it the PHB pg. 194 text doesn't imply that critical hits are exclusive to attack rolls:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter.
PHB 196 describes critical hits but never uses the words "attack roll". Reading the text above someone new to DND could reasonably assume there are other causes of critical hits.
Despite this, Jeremy made it clear that the game designers intended critical hits and attack rolls to be linked.
No, Magic Missile does not hit the target. It sails right through it. Magic Missile targets a creature, and in your mind the illusion is a creature.
Each dart hits a creature of your choice that you can see within range.
The end result is that the Magic Missile is cast, the slot is expended, but it does not hit anything unless you specified more than one creature and any of those other creatures are valid targets (non-illusionary creatures). This may give the caster reason to believe his target is not quite what he expected, and may give cause to inspect the Silent Image more closely.
As for what actually happens in the narrative when this occurs?
Let's say the caster casts magic missile and decides to hit one (unknown to him) illusionary target and two other real targets, one missile each. The missiles streak towards their targets, and hit the two real ones. The third target is an illusion and can't be hit, so the missile passes right through him. This may tip the caster off that this may be an illusion. This is the most likely scenario.
The other option is for the DM to say, "that one isn't a valid target. Try again." This, of course, tips the player off, and lets the player choose a new target for his missile. This way involves metagame information, pulls the players out of the scene, and is probably a lot less fun.
Best Answer
Death by many Magic Missiles
Let's start with when to make Death Saving Throws (PHB, 197)
So any time something gives you damage while at 0 hit points, you suffer a saving throw failure.
As quoted above in the question, the language for Magic Missile is separate per missile. Each missile strikes simultaneously, but the damage from each is separate. If we are separating damage, we are separating those Saving Throw failures.
The Concentration function is similar in that it triggers off of damage (PHB, 203):
However, it also goes on to state:
Jeremy Crawford specifically ruled on Concentration saves and Magic Missile requiring each missile to force a new save.
The real question
That leaves us the real question here as to whether or not Magic Missiles are separate sources of damage, or if the missiles hitting concurrently represent a single taking of damage.
Given that Crawford seems to believe that magic missiles are multiple sources that require a roll per source, it seems you can extrapolate that the missiles are also giving damage separately (while hitting concurrently) and thus forcing death save failures for each magic missile. The concurrent nature of the strike doesn't override the multiple deliveries of damage from separate sources.
Caveat Emptor
If you are a DM and planning to target a PC like this, you must beware of hard feelings at the table. Typically death saves are a PC thing, and if you are going to remove that by going after unconscious players then the possibility of hurt feelings is real. Most monsters are more concerned about taking out other creatures who are alive rather than double-tapping any downed creatures. If there was a real reason by the NPC to do this, then that's different - but if you're just going after unconscious players because they're easy targets to completely kill you may suffer backlash from your table.