Yes, there is a new thinking that walking or running barefoot is good for your feet and leg muscles. I would think that walking on a treadmill would be better without socks though, specially if this is your own treadmill there would be only your germs on there, but on a gym TM I would def wear socks... I'm anal like that
I would say try it for a while and see how it feels
I really don"t thing you have much to lose.
Keep us posted on your progress...