It is kinda possible, but you will have to code it in.
If everything is from the same library then all you'll need to do is add something like this.
Make a new behaviour and attach it to your animated sprite, or have a link to an animated sprite.
In the inspector code for that behaviour, add something like this
string[] clipNames = new string[sprite.anim.clips.Length];
for (int i = 0; i < sprite.anim.clips.Length; ++i)
clipNames[i] = sprite.anim.clips[i].name;
myTarget.RunClip = EditorGUILayout.Popup("Run", myTarget.RunClip, clipNames);
This code is almost entirely lifted from tk2dSpriteAnimationEditor.cs
Refer to that file for a bit more info, but this is more or less sufficient to do what you were asking.