End burner chamber pressure

No.

Shouldn't, except for local effects when the propellant is flush or almost flush with the nozzle.

The relationship follows from

GasExpulsionRate = GasProductionRate - GasRetentionRate

Now, GasProductionRate = PropDensity*BurningRateProp*BurningSurfaceArea

Define Discharge Coefficient from

GasExpulsionRate = DischargeCoefficient*P*ThroatArea

At equilibrium chamber pressure,

GasRetentionRate (equ) =

GasDensity(equ) * BurningRate(equ)*BurningSurfaceArea

Then

P = (PropDensity-GasDensity)*BurningRateProp*BurningSurfaceArea) / (DischargeCoefficient*ThroatArea)

A log/log graph burning rate v pressure is roughly linear for many propellants. For these propellants, there is an empitrical relationship,

BurningRate = a*P^n

n is called the pressure exponent; a is sometimes called the temperature coefficient. n is normally a number between 0 and 1 (though exceptions exist).

Assuming the above, defining

K = BurningSurfaceAres/NozzleThroatArea

and assuming that GasDensity(equ) Let's say that you have an end-burning APCP motor that starts out with 6" of

In theory no. In practice yes, slightly.