Do Knockdown texture walls and ceilings usually contain asbestos?
The answer is it may have asbestos in the mud that was used for the knockdown texture if built prior to 1980. 

Most earlier joint compounds did have levels of asbestos in them, I am not sure of the amount and I used to sand walls all the time in the 70’s and most of the time did not wear a mask, today any kind of sanding I use a dust mask we get smarter as we get older and realize we are not invincible. I would get the material tested to be sure as not all mud was made with asbestos.