I actually tested QAC Vs Running, and it turned out that running is actually slightly faster.
For running across a set distance on stage, the difference between running and two consecutive QACs was very small, less than 10 frames apart in my testing.
However, for attacking out of QAC, i.e QAC > Waveland > Usmash, the gap is wider, mainly due to the amount of time you can't act during a waveland. A simple run up Usmash, for example, is quite a bit faster than QAC > Waveland > Usmash.
This might seem odd, because if you've used things like QAC > Usmash before, you know that people often simply fail to react to it at all, when they probably would have reacted to you just running up, right?
It's because most of the time QAC actually takes is in the initial startup of Quick Attack, before Pikachu begins moving. If you take the startup out of the equation and just look at his travel speed, it's far superior to running. The reason people get surprised by QAC approaches is because they are looking for movement/are unfamiliar with Pikachu, and don't notice that you have started Quick Attack until Pikachu begins to move, by which time the startup lag is already over. By that time it's too late and they're punished for not noticing the startup by having far less time to react.
So yeah, run or multi-QAC across the stage as you will. The difference is pretty minor. That said, in practice QAC'ing across the stage to quickly get to an opponent has one significant advantage over running, and that is that you can start doing it from the air. Pikachu has a pretty bad horizontal airspeed and middling fallspeed, so if you're in the air just after hitting an opponent, it's often faster to QAC to the ground and then go into another QAC from that one to catch up to them rather than waiting for Pikachu to land so that you can start running.
