Yes, but only with certified treatments such as Superwash which is a very common finishing of wool.
Ordinary wool should be washed by hand, while superwash treated yarn can be machine washed on a wool program.
It's recommend not to use fabric softener when washing superwash yarn. The fibers will then lose their elasticity.
All our suppliers are obliged to provide detailed information including "product sheets" with an overview of which chemicals are used in this process.