Maybe- if you get enough roots without damaging them when you dig and if they like the conditions of the new place. I have done so with success with a number of kinds of gingers- Torches, alpinias, kaempferias, some others- butterfly's can be a little finiky, but I have had sucess with them as well. Try it- the worst that can happen is a stem goes and you have to wait for a new one to come up.

The Alpinias are easy to keep fairly good looking.
Remember that this time of year certain gingers go dormant anyway; like Curcuma (hidden gingers)and butterflies. This really is the time of year to move'em.
Mike