Phil
I have turkeys moving through my beds a few times during the growing season. They scratch around a little occasionally in the beds but not often, or sometimes next to the beds. But they have never done any real damage to my plants. The woods around here are huge and the turkeys have plenty of other places to investigate. And in the winter we usually have deep snow covering the beds from late Nov. through early April to protect the bed from turkeys. And most of Nov. the ground is frozen solid.
I do know, if they Continue to scratch the soil in your beds on a regular basis, they will cause damage and you will need to do something. I think putting chicken wire up just tells everyone that your growing something. Which depending on where your beds are, may not be a good idea. although if it's in an area where others are not going to see it, it would probably be your best bet.
Maybe someone else here has a more sure solution.
Good luck.
classicfur