Oh yea hay is really good not only for their teeth (rodent's teeth never stop growing) but its also good to help keep around their natural habits. I always start out with putting the hay on a marble tile I have, and the next time I come around its spread out all over the place! Chins are also foragers so you'll see them 'dig' in the hay and eat it. I dont' think its a problem at the bottom just make sure to look out for soiled spots since that can make them sick.
Your new guy sounds a lot like my new guy! He loves being held too and falls asleep on you, we call him 'lumpy' sometimes because hes just like a big lump of fur you can hold! Thats so awesome you and your chin are getting along so well already, its an amazing bond!
Oh and also just make sure you're room is chin-proofed if you keep your cage open, or when I keep it open I have giant cardboard walls I put around and make a play area. I posted the pics up in a diff topic I can give you the link if you want as an idea
