Not exactly the Eddington limit only relates mass to the maximum luminosity possible for that mass. It does not, itself, require a specific type of power source for that luminosity but just contrasts the outward radiant energy against the inward gravitational energy on the star.
The fact that stable main sequence stars (like our Sun) are in a general state of Hydrostatic equilibrium, outward pressure balanced by inward pressure, indicates the most probable source for the energy of that outward pressure is directly related to the mass of the star. Internal fusion fits those requirements and the observation. But don’t let that stop you, propose any power source that you like and the Eddington limit would still apply (within its constraints), unless of course you are proposing an external power source that would require incoming energetic particles to supply that power and thus increases inward pressure, then you would need a greater output to balance that incoming pressure plus gravity, which would require more energetic, or more, incoming particles to supply that power, increasing the inward pressure, requiring greater output, more inward pressure, requiring greater output, more inward pressure, requiring greater output, more inward pressure……..
