ps3, dual booting and online play through psn

so i was wondering, if you have a ps3 able to dual boot, would youi then be able to install games to the internal HD as psn games on the CFW. Then boot the OFW and play the games while using psn. or does the dual booting separate the file system and whats installed.
to be clear "install as psn game"= using the eboot method

IF you had a dual boot set up you would need to play legit blu-rays for OFW.

I'm not sure if there is a way to Dual boot. E3 showed off a video of their dongle doing this, but I'm not sure if that ever became a reality.