If you rabbit proof the rest of the house and dont mind her possibly peeing in corners to mark her territory and potentially opening yourself up to allowing her to come out more often, then I would say go for it! The more time she spends with you, the more bonded she will become to you.
My bun has her own 12×9 room. The door stays shut when we are asleep and when we are both away. If we stay gone longer than normal, like if we go out, and throw off her routine, she will not come out of her room if the door is left open. We have to go in and get her and bring her out ourselves.
Blossom might not be leaving the room because she feels safe in there and doesn’t want to venture outside her comfort zone. She might also see the rest of the house as your territory and the playroom as hers. So she might be uncomfortable overstepping her bounds. She may just not be aware of the rest of the house. My bun never goes outside and therefore never seems to be interested in the magic door that we disappear into for hours.
The key will be to bunny proof!!!