RNP, assuming that I have correctly understood your question, then ‘in theory’, your theory would be correct.
However, I suspect that there are several embedded assumptions which would invalidate it in practice.
For nil, or low levels of reverse where the component of deceleration from reverse thrust is less than the commanded auto-brake level, then the auto-brake will control the value of deceleration and provide the same distance.
This assumes that the level of auto-brake deceleration is indeed constant. It might not be depending on brake system characteristics and/or capability, e.g. the level of braking deceleration might reduce with speed (but then the low level of reverse might make up this shortfall).
Higher reverse thrusts might create a component of deceleration greater than that required by auto-brake and thus the runway landing distance will be proportionally shorter depending on the level of reverse used and/or auto-brake level selected, but this depends on how the effectiveness of reverse reduces with speed.
The above does not considered the any aerodynamic effects, or the runway surface; even dry runways have a range of surface characteristics and frictional qualities, any one of which would change the runway landing distance.
Thus I suspect for the braking question, like many things in aviation, there are few ‘absolute’ theories; the important aspects are to understand the assumptions within the ‘theory’, and ask the ‘right’ questions in operation.
See here for info:
FSF ALAR Tool Kit Briefing Notes Chap 8.4. Braking Devices. Figs 3 & 4 indicates some of the variables.
Also see:
Flt Ops / Flying Technique … “Landing on Slippery Runways”.