By removing the coil.. you in essence are installing a totally new coil.. Just a pretempered one, kinda like when we torched all the wire before building, for clearomiser like
nautilus and Protank. Just the act of removing the coil will create potential new hot spots or hot legs. Not as bad as fresh wire.
Can it be done, YES. Will it work afterwards, maybe, but not as good as if you had left it be.. I have tried this. Not for rewicking, but to move a coil to a different atty. It works, just not real well and not everytime.