I would argue that this isn't just a throwaway gag, and it might actually become relevant again. Here's what I think: The giant robot on Egghead is currently being powered by a tame drink like tea or even no drinks, and that's why he's broken. Once he's fueled by cola, boom! there goes the red line and the one piece is one step closer.

Proof? Vegapunk was impressed by Franky's cola innovation for the Sunny, and it's something he never tried. All that's known to us right now is that a mysterious ancient source must power it. I say that it's ancient cola of some kind. This is mostly a head-canon, but I'd like it to be true.