It depends. Usually areas under big pieces of furniture, such as a dresser are not that dirty as they do not get a lot of foot traffic. Moreover, if you get these areas cleaned, you will generally have to wait until the carpet is dry before replacing the furniture.
Our carpet cleaners only move small pieces of furniture when necessary, such as chairs and coffee tables as long as they do not have anything else on top of them and they are in sound condition. For these pieces of furniture we also use plasting tabs or foam pads that we place under the furniture legs to prevent rust/stains transfering to the carpet before it dries.
We always exercise caution. All furniture moving is done at your own risk due to the varied condition of furniture, in general. You will also be responsible for replacing any moved furniture that does not get put back in place. Please be careful when moving furniture, we are not liable for any accidents, damage or health issues caused by you moving said furniture.