Yes carpet beetles will eat wood along with any other things they might come into contact with.
Carpet beetles will not only eat wood but also bedding, fabrics, carpet and anything else they can get too.
Sometimes you might have another type of beetle in your home that is eating the wood too which is called a wood beetle.
The wood beetle only eats wood though so if you have beetles in your house that are eating wood and other things including fabric and bedding or carpet then you have carpet beetles.
But if the beetles are only eating wood in your house then you likely have wood beetles instead.
Carpet beetles will not bite humans like bed bugs will although they can leave a rash or itchy spot on a humans skin if the carpet beetle crawls across the humans skin.