Well, my first though would be no. However, it would really depend on the material used! Wool wouldn't be a good idea IMO. I think a knitted strap would be quite springy.
I suppose it would okay if you wanted to put some bounce into a given riff
Also, the kintted neck straps would cut into your neck, leaving little knitted patterns in your skin. I think the material of a neck-strap needs to be smooth.
I could see mouthpiece bags and crook bags catching on, though.
Since I started playing the Sax I've had Saxxy socks every Christmas and Birthday Not too mention ties, cufflinks, T-Shirts, etc ... :shocked: I keep telling them I do have other interests you know Then this Christmas I got a Piano Tie and a Guitar T-Shirt ))