If it is legal to use a rifle where you hunt (I don't have any idea), and you feel like hunting say with a 22 LR or a 22 WMR, I don't feel that is unsportsmanlike. I'm assuming head/neck shots only, meaning you'll need to call them in close anyway. I wouldn't shoot for the body with the LR, maybe with the WMR, but you'd need to be very familiar with turkey anatomy to put a killing shot on one that will also result in a recovery of the bird. You may find the rifle more frustrating to start with, as a shotgun leaves a little more room for error. Bottom line is, the weapon does not make you take an unsportsmanlike shot.

I watched a a TV show with Ray Eye and another hunter. That guy (not Ray) took 2 bad shots on film with a shotgun. After each one he cussed himself saying he never should have shot, couldn't really see the bird, just fired where he thought it was.