Yes and No.
Not because it isn't modelled, but simply because we fly around with our throttles at 100% all the time. In a real life situation, carrying more weight would force you to increase your throttle setting and hence your fuel usage just to maintain cruise flight. In AH, we are all at 100% anyway, so we are burning the same amount of fuel anyway, it's just a matter of how fast we fly or climb using that power. Weight has the right effect on the flight model, we just have a different situation in terms of throttle settings. In WWII, it was long stretches of boredom punctuated by very brief bits of action. Since in AH we want action most of the time, the game really has to be set up this way.
I think the difference is that the strategic bombers generally had huge fuel loads anyway, and even with the fuel multiplier we aren't likely to hit those limits due to time constraints and the smaller size of the game world.