In the past I had thrown a blanket over the crate on cold nights and to block out light on the hopes she would let us sleep a little longer in the morning. The crate was always in the room with us.
We never had an issue with ours messing with the blanket. However, we have a huge transportation style crate and not the mesh cage.
Ours always had to know where we were at all times. She was good at laying in the doorway to whatever room we were in so we couldn't escape without her knowing.