Yes, hatching the required dragon the moment you get it, way before you are asked to do so, has been okay.
HOWEVER, as this may change without warning, I usually won't hatch it unless I absolutely have to; can you imagine having to wade through a dozen Elder dragons to get this one again if they suddenly feel that we should only do the hatching when they ask us to?
That being said, the wordings at Day 6 for each of the Tales have been, "Hatch a
<Insert Name> Dragon". They have always treated this like the "Raise
<Insert name> Dragon to
<n> level" acts where we were allowed to raise the specified dragon to the required level long before it is even required. BUT, if the developers made an adjustment to the algorithm to require the hatching to occur after we are asked to do so, then the play would be just like the "Craft and decorate with a
whatever" acts, where you may craft the item early, but cannot put it out before you are asked to do so.
Boy! That was confusing