You would probably need to modify the firmware to achieve what you want as the file system (FAT) is initialised when the sd card is inserted (note the small micro switch on the socket) triggers an interrupt, which does quite a lot behind the scenes.
So that's how it works!
It may be easier for you to create a a shield which has some flash on it which you can use as you want then use that as a buffer to write to the SD card.
I used an ArduinoMega2560, with a dataflash chip over SPI. That worked really well. But addressing a Dataflash, also means that reading and writing only works in pages of 512 bytes. and that can get complicated and inefficient really easy, when you need to address one specific byte of an image..
Reading and writing single bytes is very easy thanks to the filestream... but it's too dam slow.
How would one tingle with the firmware? is there an example i could look at?