Sure, you can manipulate the vertices in a path attachment (not the path constraint).
PathAttachment vertices
Note a path is an attachment and all attachments are stateless and shared across skeletons. If you change the path attachment vertices, it will affect all skeleton instances. If you only have one skeleton using the skeleton data then that doesn't matter for you.
Another way to do it is to weight the path to bones, then move the bones. This doesn't have a problem with multiple skeleton instances, because each has their own bones. It is also usually pretty easy to position a bone in your game. Manipulating vertices is different if your path has weights.
Note you may not need IK constraints like stretchyman. A bone for each path vertex may be sufficient.
Depending on the movement you need, you may be able to use an animation. Eg, your animation could be with the neck all the way stretched, then you can blend the animation from 0 to 100% using TrackEntry alpha
.