With a pH near 11, I would not suggest using it on wool. Wool should be cleaned with a neutral or slightly acid cleaning agent, somewhere between 6.0 and 8.5 is ideal for not harming the wool. Slightly higher p H is OK if it is thoroughly rinsed in a timely manner.
The cleaning agent is able to react with the outer layer of the wool called the cuticle or epidermis. This begins to break it down. Depending upon how high the pH is and how long the chemical is on the fiber, the break down could be so minor as to only be seen under a microscope or it could become very obvious.
As the fiber breaks down, it gets weaker and bits of will break off under foot traffic or vacuuming. Over time, some of the pile is lost.
The difference could be insignificant to s low value rug but a rug worth tens of thousands could lose most of its value.