If an aircraft were to climb at constant MAP, the reducing atmospheric pressure would cause exhaust back-pressure to decrease. This would make it easier for the gases to flow through the engine. We would have a constant pressure (the MAP) pushing the mixture into the cylinders and a reducing exhaust back-pressure opposing the outflow of exhaust gas. This would increase the mixture volumetric flow rate through the engine. In addition to this, the constant MAP would maintain constant mixture density. The overall effect would be increases in air mass flow rate, fuel mass flow rate, and power output.
If the same aircraft were to climb with constant throttle angle (full throttle for example) both MAP and exhaust back-pressure would reduce at the same rate. Reducing MAP would reduce the density of the incoming mixture. And because both MAP and back-pressure would reduce at the same rate, there would be little if any increase, and more probably a decrease in volumetric efficiency. Logically the volumetric flow rate must decrease to zero as we climb out of the top of the atmosphere (if we could do so). The overall effect would decreases in air mass flow rate and power output.
To see what would happen to fuel flow rate we must look at what would be going on in the choke tube (I am assuming a float type carb). By accelerating the airflow, the choke tube produces a drop in static pressure. It is this pressure drop that causes fuel to flow through the main jet. The fuel flow rate through the main jet is proportional to the square root of the pressure drop across it. In effect this means the square root of the float chamber pressure minus the pressure at the throat of the choke tube.
The choke tube is a simple venturi, in which the throat is narrower than the inlet. The ratio of air velocity at the throat is inversely proportional to the ratio of the area of the throat to that of the inlet. So if for example the throat area is ¾ that of the inlet then the velocity at the throat is 4/3 of that at the inlet. If we assume that air density is constant then dynamic pressure at the throat, which is proportional to velocity squared would be 16/9 that at the inlet. These ratios are all determined by the geometry of the choke tube, so they do not vary with altitude.
But air density decreases with increasing altitude, so for a given choke tube geometry the absolute values of these pressure changes will decrease as altitude increases. Suppose for example that for some given choke tube geometry we had 15 psi ambient pressure and a 5 psi pressure drop at the throat at mean sea level. If we were to climb to an altitude where ambient is 5 psi we would not get zero at the throat. The absolute value of the pressure drop would have decreased.
And it is the square root of the absolute pressure difference across the main jet that determines the fuel flow rate. As the absolute value of the pressure drop decreases, so does the fuel flow rate. So fuel flow rate would decrease as altitude increased.
The gradual enrichment of the mixture is caused by the fact that as altitude increases, the density of the air decreases but that of the fuel remains more-or-less constant. So as altitude increases, the air mass flow rate decreases faster than the fuel flow rate.
So as altitude increases with constant full throttle setting fuel mass flow rate, air mass flow rate and power output will all decrease.