I am very cautious about them ingesting non-food items. You would have to be sure that the mats are not treated for a start. Best to stick to mats that are made especially for bunnies.
It would all depend on if your bunny is a chewer, if you mean chewing the rug I would recommend going with rabbit toys and rug specially for bunnies. If you are after a rug your bunny can be up on and use as flooring and not a chewer it will work.
It’s not like my own bunnies are chewing up the door rug and the other rugs in the house they step on