This is an interesting question, and one that trips up a lot of people when they experiment with electromagnets (which is what the rotor of the motor is.)
The simple answer is yes, more coils increases the resistance of the electromagnet.
Because this experiment uses a (roughly) fixed voltage on the rotor, the current through the rotor decreases as you add more coils. Important variables for an electromagnet's magnetic field strength are the number of coils and the current through the coils. As you can see, with a fixed voltage, changing the number of coils affects TWO variables. A good science experiment tries to control as many variables as possible, so that you're only measuring one effect at a time. The equation for the magnetic strength of the coil:
B is practically constant and is given by
B = (u0 * N * i ) / l
where μ0 is the magnetic constant, N the number of turns, i the current and l the length of the coil.