In short, in the editor, no.
If you came from Flash, you may have to change the way you think about animations that play at the same time. In Spine, animations aren't "inside" other animations. But multiple animations can be played at the same time.
You can have one set of animations that just animate idle melee and running.
And you have a second set of animations that just animate the sword glowing.
Play them at the same time at runtime and it will work.
Unfortunately, there's no way to preview this yet in the Spine editor.