I have actually done this, but it's been quite a while.
As far as I know, it is safe, I couldn't find really anything online about binding with a scarf and if it's safe or not but I feel like it could be (if anyone knows more about this than I do, feel free to add something) but if the scarf is thicker then you may want to either choose a different scarf, or put on a larger shirt / jacket to hide the scarf.
Also, if at anytime the scarf seems too tight or your breathing becomes off, loosen the scarf a little, or take it off completely.
Sending you good vibes, and I hope you're having a nice day <3