If you are talking about reusing the wire and rewinding it on a different core, yes. I do that all of the time. I'll take the chokes out of old computer power supplies and wrap the the magnet wire around a sturdy section of coaxial cable to make a common mode choke for my oscilloscope. I use that to monitor my radio power out put and modulation.
As long as you are careful while unwinding the field coils you should be fine.