Yes, and it’s a common practice.
What you would want to do, once you finish the rigging process, is to create an autorig of it so you can quickly create the very same rig on different size. Also, what could work is if you just uniformly scale the same rig and reconnect deformations, but mostly it won’t work as your other characters/sizes probably aren’t uniformly scaled, but it would be just a quick and dirty adjustment that could work in some cases.
If the change of the same character is not that big, using blendshape with new mesh could work, but I would strongly suggest to remove deformation nodes from mesh, modify mesh, reconnect deformations to it.
Since your rig is the same as your master rig, sharing animations is simple and straight forward.