Well, the firmware update could "theoretically" make a difference to frame rate, if it improved disc IO and the frame rate problem was somehow caused by delays streaming in data. That seems extremely unlikely though as that usually just causes object or texture pop in, frame rate is usually down to the CPU or GPU getting temporarily bogged down. Its possible that a firmware update could improve game loading speed marginally, if they somehow improve the optical drive performance. That would be more a case of fixing an existing bug though and unlikely to be a night/day difference.
The speed of the internal memory seems to have zero effect on disc based games (it shouldn't). I downloaded something from the eShop and had it download and install in the background while I was playing LEGO City Undercover. The game ran identical to usual and I didn't even realise it had started installing until I tried to go back to the home screen and the whole console just hung, as it was unable to load the UI back in. I just left it alone and after 5 minutes or so (once it had finished installing) everything was back to normal.
I really don't get why some people think a firmware update can fix frame rate or game loading times. Frame rate can be improved by GAME updates making the game engine more efficient, load times can't really be changed unless they allowed partial copying of the disc content on the internal memory or HDD. The speed of loading off the disc is dictated by how they laid out and compressed the data in the first place, not something you can fix after the disc has been manufactured.