This is a question I have been struggling with for the last 3 months. You are right to be worried. My puppy was placed in the crate without any bedding since I was worried about him chewing it/eating it. I'm more concerned with his safety than his comfort...BUT, I decided to give it a try last week, since he is 5 months old and hasn't really chewed anything. The first night went well, but the second night he got frustrated at 5AM and started to tear into the bed. I woke up and took it out of the crate. I have not done anything since then. I have been told to try letting him out of the crate (i.e., leave the crate open, but put a bed in the room for him to sleep on). Not sure about this...I guess I will give it a try.
I did not cover the crate, now at 5 months, he sleeps from 10 PM to 6 AM every night. I'm happy with that, I think he would go longer if I had the crate covered, but again, I worry he may pull the cover in and eat it. So, no cover for us.