I was a little disappointed by this quest as a Dalish mage. I was asking Morrigan questions I figured my own character would know far more about and would actually provide more insight on, besides the odd "my clan prayed to him when we hunted. deeeeeeerp.. AND THAT'S ALL I KNOW!"
No, it was mostly my inquisitor: "WHO DIS ELBEN GOD GUIYS?"
Morrigan, in her haughty knows-it-all voice: "Why that's the elven god Falon'Din, derp-a-derp, inquisitor, you ignorant dummy!"
Solas: "I know more than you *koff* was-actually-there *koff* and Falon'Din was the biggest butthead evar. Derpderp, Morrigan."
"Is that so, Solas? I know so much, I'm practically elf-blooded! Why, if elven history was modern day Japanese culture, I'd be the elvish wizard-princess super Otaku of all!"
Blah. Anyway, I figured my Elven Inquisitor would drink from the well, but there wasn't anything that encouraged her to drink in regards to her heritage, even Abelas didn't give two shakes of a rats butt, and was basically like, "whatevs. im off to go be sads somewhere guys."
So, I let Morrigan drink all the pond water of glowy elfy knowledges because it seems like that's what the developers/writers were guiding us towards.
It ended up being kinda sad and funny at the same time when Flemeth came to call, so I suppose it's best that Morrigan drinks the water.
So, my canon: Morrigan the elf Otaku drinks the elf water.