There's a discussion of that programmer elsewhere, and it's decent, should do the job for you. Make sure that the bios file is the raw image if you're writing it with a programmer, not some other format that needs to be interpreted by the firmware installer, then you're probably alright.
While it's unlikely in this case, I know some motherboard vendors were able to supply preprogrammed BIOS chips for their boards in the past - I think this is only likely if they are also socketed, which basically no laptop ones are, but it could be worth a customer service ticket.