Is there a relationship between turbojet engine rpm (N1 & N2) and fuel consumption rate?
Yes, these need to be roughly proportional for the engine to work, and will move towards an equilibrium if they are not.

The compressor provides the air for the combustion, and injecting more fuel will only generate a little extra power, which however increases the turbine speed, increasing air intake, which will allow more fuel to be burned, again increasing available power and so on.

In practice, if the air/fuel mixture is way off, compressor surges can happen, so in modern systems the engine computer will limit fuel flow.