I dont think it would, as most general users wouldn’t know how to turn it off, and they would keep their computers up to date.
Well, as long as you mention that JS is required for the app to work upon signing up for the membership, this is just for legalities. I see no problem with it!
Besides; they get a two week free trial so if it doesn’t work, then can always cancel shrug.
JQuery is awesome though; really helps when creating user interfaces.