Pets only heal, so no they can't critical hit. But it would be great if they could critical heal, but I don't think that is possible with spirite. Good idea though.
I've done critical hits with Spritely quite a few times. Any healing/damage spell can critical, it's just most people tend to use Satyr and Pixie for non-life primaries. I know that when my pet casts spritely, I get boosted on it, but I also know that it's because of my gear, and not them, but this shows their spells will work off of our stats. If they didn't then the spells wouldn't be boostable.
But then again, this is just my thoughts. I'd love to see what others think :)
If pets go off of our stats to at the very least boost their heals then why can't they go off of our stats to critical a heal too? It would make more sense to me personally to have them go off of ALL of our stats. But that's just me.