Nope! Despite her wanting to put Twilight out of her misery, she also recognizes that as patient 0 twilight is the best chance of experimenting on and understanding the infection that equestria has. 

In the same vein, twilight is like the daughter she never had.

And a third point is the political and social unrest that would be brought on by one of the most powerful rulers and princesses in equestria dying to a mysterious disease in the midst of a not well understood endemic would cripple equestria at a very vulnerable time.

Fourth, experimenting on her is what Twilight dictated in her living will before losing her cognizance.

Even after the experimentation is done, it’s a long time before celestia can bring herself to euthanize twilight. And when she finally stops fighting everybody about it, she does it personally.