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If it use the mass of the displaced fluid in the calculation above,
am I already accounting for some of the "drag" force which is
normally accounted for in this velocity squared term?
That's a smart question. In this business, there are very often multiple
ways of explaining the same thing, such that when you try to quantify it
you run the risk of counting something and its synonym as two things when
really there is only one thing.
In this case it comes down to a question of terminology: By convention the
unadorned term "drag" includes everything that acts like drag.
Also note that everything is /indirectly/ dependent on everything else. For
example, even if you think the drag does not directly depend on the displaced
mass, it indirectly depends, because it is related to the overall size of the
aircraft, and drag certainly depends on size. At the end of the day the most
you can achieve is consistency, i.e. a consistent set of numbers for the size,
mass, acceleration, velocity-field, pressure-field, et cetera. You might wish
for some nice simple separation of variables, but you're not going to get it.