I'm having some doubts here, you might see some small effect

However, when you're looking at electric motors they always have 2 separate coils, or a coil and a permanent magnet. (The cage in a squirrel cage induction motor is also a coil).
10 minutes later...
So I grabbed an electromagnet with a 120Ohm coil and a 120Ohm resistor and put 20V over it, which resulted in a current of 80mA. I used the resistor to have a higher (and symmetrical) impedance from the 20V power supply.
Adjusted my rigol scope to AC coupling to see differences on the 10V over the coil and then I started pulling the iron core out of the magnet like a madman and pushing it back.
Whenever I pulled the iron core out of the magnet the voltage over the electromagnet dipped by 4V, and when the iron core was pushed back into the magnet I had a positive spike on the elctromagnet of also around 4V. Such an even has a duration of around 30ms to 40ms.
So you are right. A change in the amount of iron within the inductor changes the flux and with that you see voltage & current spikes.