Since I'm away from my PC and this fell out of the doodle game submission window (which I'll clear up now, will just be on the fridays I open them up!), I'll describe it for now!
I imagine at first, not much would happen, BUBBLGUM might slow down just a little bit as she optimizes herself to move that much data all at once, only to soon reach the complete slowdown of her systems as TUMM does its thing to account for the now terabytes of data getting fed into the machines storage all at once. It wouldn't be a fast process either... I don't know if it would be better for most of the sensors that allow BUBBLGUM to perceive the outside world to be on or off while the process is happening, but by the end of it, this gel liner has pushed the HIFLEX abdomen to its limits, spilling out and rolling over itself in all directions, likely taking up a room of space in the process.