Can a Pokemon in X/Y relearn an egg move it never knew?

Question

I want my Delphox to learn Hypnosis, but it never knew it before.
Would it be possible for the Move Reminder to teach it to my Precio--I mean, my Delphox?

Answer 1

No, if you want a Pokémon to re-learn an Egg Move, it has to have learnt the Egg Move in the first place hence the name "Move Reminder".

And yes you can re-learn a Pokémon an Egg Move, if they have learnt it before and forgotten it.

>In Generation VI, any Pokémon bred or obtained in a Generation VI game may also be taught any move it knew when it hatched or was obtained. This includes Egg moves, Volt Tackle bred onto Pichu, and event-exclusive moves such as the Pokémon Center Tokyo Bay Inkay's Happy Hour.

Source: Experience and Bulbapedia

Answer 2

No,
the move relearner simply teaches Pokemon moves they could have learned a a level up move at a lower level, this can be useful if your Pokemon level up twice and missed a move it should have learned when it evolved, (it is also used as a way for fully evolved Pokemon to learn moves that would be otherwise unavailable). The moves that a Pokemon can remember are unaffected by moves that where actually learned in the past. For example in SoulSilver I taught my Arbok TM 23 iron tail which I later accidentally deleted. When a went to the move relearner and to my dismay, it was unable to relearn iron tail.

Answer 3

To put it simple, no. The only way for it to have hypnosis is if it had it when it hatched, or if it already has it.