Coincidentally this feature has been added to Timelines, and will be landing at the start of the next beta cycle.
It was implemented by means of the "initial frame" property of the Sprite plugin. This means a timeline will interpolate the value of that property and assign a new frame as the timeline progresses. There will be a few things to look at for when using it.
Because the timeline will be changing the frame of the animation, the plugin itself will not be playing the animation, so all triggers and conditions that the plugin would normally execute, will not happen. Instead you will need to rely on similar triggers and conditions on the timeline itself.
The only exception to this, is the On frame changed trigger that the sprite plugin will execute while being animated by a timeline.
Furthermore, attempting to play a Sprite animation normally while it's current frame is modified by a timeline will result in strange behaviour. So it will be a case of picking one or the other, but not both.
I doubt this will be added to Tweens, it is a rather specific behaviour and while it is possible to implement it, it would be a pretty ugly monkey patch.