Focusing on the simpler of the two, the BIOS boot, the answer is no. To quote this IBM reference IBM link
Historical issues limit the size of a user-supplied bootloader program to slightly less than 512 bytes. Since this isn't enough space to implement all the possible device drivers that might be required to access different displays and storage devices, it's necessary for the BIOS to install standardized software interfaces for all installed, recognized hardware that might be required by the bootloader.
The system needs to load device drivers that will not fit into the memory space of the firmware and thus the OS is indeed present during the stage of boot involved in discovering the drives.