I had a message that requested a booking for the next day. I approved the booking and the owner and I have arranged a drop off time. However, she has not accepted the booking through Rover and has not paid. I haven't given her the address, but can she see it on my profile and just drop the dog off without accepting the booking?
If I understand correctly, you did not have time for a Meet and Greet. Once you have had a Meet and Greet, the client will have your address.
If the client shows up without making payment, don't let them leave their pet with you until they have done so. You are not covered by Rover's insurance unless they have paid for the stay.
I just went through this the other day.. it was a 7am dropoff and the owner finally messaged me at midnight saying nevermind, it was pretty frustrating.
So your address isn't on your profile until you both have accepted or you've done the meet and greet. As Carmen said, don't take the dog until it is officially accepted so that you can be under Rover insurance and everything is done properly.
To answer your question, without a meet and greet the owner will not have your address until she accepts the booking.