I'd say no, it wouldn't crit...
But, only because it is a spell -- and spells only do what they say they do.
And, nowhere does it state that a spell like a Fireball has a chance to crit -- however, due to Unconsciousness, (which causes ALL DEX and STR saves to fail) they would automatically take FULL damage.
I would say unless it is an ATTACK ACTION (using something with a crit range), then I would disallow any crit chances. Spells are their own weird beast.
I believe that "if you're making an attack roll, you're making an attack roll" is misapplied to spells -- I believe that quote is supposed to refer to physical attacks/feats/special maneuvers --especially when you're improvising something on the fly.
I disagree with the assertions that just because spells don't have attack rolls, they are not attacks -- they are "Spell Attacks"...whose rules are different -- only going by their descriptions and if those descriptions forgo an attack roll, so be it (e.g. Magic Missile is an attack, even though it has no attack roll). That doesn't mean they aren't attacks -- if it causes damage, I would classify it as an attack -- though I would call it a "Spell Attack".
I'm going to say that Spells fall into a few general categories, Attack, Buffs/Debuffs, Healing, Utility, and Situational.
Attack spells cause damage and directly attack enemies.
Buffs/Debuffs either boost your or your teams abilities or disadvantage your foes (but don't necessarily cause damage)
Healing spells restore HP or functionality
Utility are those spells that do things that are useful but don't fit those other categories -- also some of the "ritual" capable spells.
Situational spells are a subcategory of Utility, ones that are useful only in certain situations where they're excellent.