The rocket equation doesn't account for thrust. It's terms are mass and ISP (or exhaust velocity).
>If this tech lowers the weight of the first stage, it might actually RAISE the ISP of the rocket overall, even if it lowers the ISP of the engine itself.
ISP is depends only on exhaust velocity. Changing the mass of the rocket cannot effect it.
Only sort of true. If you naively apply the rocket equation like you're imagining, you would predict a nonzero final velocity for a hypothetical rocket that has enormous ISP but thrust less than its weight. This is true if the rocket is starting out in orbit, but it's totally wrong when you're on the ground. Starting from the ground, you also have to fight gravity, so you care more about (thrust - weight) / mass.
https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
If you want to be more specific, e.g. include gravity then you can't say "the rocket equation".
> If you want to be more specific, e.g. include gravity
> then you can't say "the rocket equation".
[1] https://www.nasa.gov/mission_pages/station/expeditions/exped...
It's very accurate when those things contribute little, and totally inadequate for modeling spaceflight if any are significant.
There are more complex versions that account for those things, but 'the rocket equation' is always understood to mean Tsiolkovsky's equation.