Tom,
I would recommend not getting all worried about BPO's. Have who ever is in direct contact with the Lender make sure that you are contacted to schedule any BPO. When a BPO is ordered, the agent then will call you to set up the appointment. (About 90% of the time we get called. Only about 10% or less of the time do BPO agents just go striaght out to the property.)
We have negotiated properties where the Lender(s) only ordered 1 BPO. We also have had many where several BPO's have been ordered.
Unlike smitlit, most of our clients have the property listed from day one. As for the Listing price affecting the BPO. Yes, it can, yet again sometimes. It all depends. You should be focusing your negotiations on justifying the offer, not so much about the BPO. The BPO is only 1 in a series of numbers used by any Lender to calculate how much they will SHort the property for.