People do. We don't recommend it unless you (or a stylist) really know what you're doing.
Keep in mind that in most cases this hair has already been HEAVILY color processed. Unless the hair is labeled "virgin", you can guarantee that it has been treated in any number of ways to approximate a certain texture, color, or style. Non-Virgin WILL NOT react to hair dye the way that unprocessed hair might.
What about Jon Reanu's Elite colors?
Here is what they have to say about that:
There you have it! Even in this line, only their colors labeled with an "RN" can be colored beyond what is done to the hair in the factory.
It's your hair. Customize it however you like. Just know that there is risk involved and you could damage your wig...so be super careful and do your homework before dying ANYTHING.