More or less, yes. What matters is where the voltage drop is occurring. If the voltage drop is only at the fuse box itself due to an undersized feed, but the battery is maintaining ~14 volts the entire time, then moving the lights to run directly off the battery will have a positive effect, since they will no longer be subject to the drops affecting the fuse box.
However, if the voltage drop is due to the PCM briefly turning off the alternator, or the alternator not yet having caught up to the demand, that drop will be at the battery itself, so it effects everything in the vehicle. Moving the lights directly to the battery wouldn't have an effect there, since they would still be affected by the same drop.
In the first video it occurred in conjunction with the AC compressor turning on, which I call normal operation for these cars. My 2000 Regal did that and my parents 97 Lumina always did the same thing. The 2nd video was harder to tell, but it seemingly always happening around the same speed when coasting down makes me think that's when the car is coming out of it's deceleration fuel cut off, and the alternator output is briefly being cut to make the transition back to the IAC smoother. Older vehicles didn't experience this in the same manner, as the alternators weren't controlled by the PCM. Newer vehicles with electronic throttle bodies don't seem to experience this either as the PCM has full control over the throttle itself. I really don't think there is an issue that needs solving. If you want to keep the headlights from showing the effects, you could look at switching to LEDs. The LED chips typically run at less than 12 volts, so they have a voltage regulator to keep things in check. This would prevent them from dimming whenever the vehicle voltage fluctuates slightly.
Also, ignore what I was mentioning earlier about the ABS. The ABS kicking in will cause the lights to dim briefly due to the load, but after seeing the driving video, i don't think that's what's happening here.