The PCs are testing the rumor—so make a choice!

Your campaign is a custom one, so while purify food and drink maybe should apply only to food and drink that's consumable by a creature of the race casting the spell or by the god that grants the spell or something, that doesn't mean the campaign's pixies aren't actually food for everybody.

In other words, the PCs have heard rumors of a creature that gains power via snacking on pixies, so when the PCs cast purify food and drink on a pixie corpse and they or their goat friend is about to dig in, you've to decide if those rumors of greatness through faerie feasting are true. (Fun Fact: PCs—and players!—will likely be disappointed if such rumors are untrue.)

If the rumors aren't true, the spell simply fails. No harm, no foul, no pixie picnic, no übergoat. All done.

If the rumors are true, then you've to decide how true. Can anyone partake of this pixie power-up? Need the pixie be alive? (Ew.) Some degree of fresh? (A day sounds good.) Must the entire pixie be consumed? ("Pixie wings taste like fruit roll-ups!") Is that healthy? (Likely not.) Must pixie be prepared a certain way? ("It must be served... on a stick!") Do a certain number need to be consumed to gain ultimate pixie power? And so on. Then the spell works, but, maybe, after consuming the pixie, the PCs are left wondering why their goat has a bellyache instead of awesome pixie powers.

This is your campaign, and—to challenge the frame a bit—this is less about how the spell purify food and drink works and more about the effects of pixie-eating in your campaign. That is, determine event's outcome and steps required to reach it first, and the question about the spell likely answers itself.

Possibly yes, but in this case, no.

It's pretty reasonable to assert that purify food and drink would remove hazards like bone slivers from food. Personally, I'd rule that is does, since a spell designed to make food safe to eat should, you know, make food safe to eat. However, it's a reasonable ruling to make that the spell only affects "poison and disease", since those are the only effects mentioned in the spell.

However, since you're playing Hoard of the Dragon Queen, this is all immaterial. Spoilers ahead.

On page 38, in the Who's Your Friend section, Jamna Gleamsilver approaches the players and tells them that they have bone slivers in their gruel. There are no bone slivers in the gruel, but there's one stuck to her knife, which she dislodges into the player's gruel in order to get the players to trust her. There aren't any bone slivers to purify, and since the sliver wasn't in the gruel until Jamna stuck her knife in it, there was none to purify beforehand either.

To give a non-spoilery summary: in this case, purify food and drink would not have prevented the NPC from finding bone slivers in your food.