AC through inductance only
The concept of emf is artificial, it's created to have a single systematic formal representation to voltages which are caused by different physical reasons. We need it to have a solid circuit theory. 

Inductive emf helps us to forget that physically induction induction happens in magnetic fields as well inside and outside of the conductor. Induction law states that if  magnetic field somewhere changes for any reason, then at the same place there exists an electric field which can be calculated by using the following equation (a 3D vector differential equation). If the change of the magnetic field happened to be caused by changing current in a conductor, the generated electric field is always directed to resist the change of the current. We model it with a voltage source which is thought to reside inside the conductor and we call it inductive emf. The well known equation for that emf has been known nearly 200 years.

But the inductively generated electric field is as well inside and outside the conductor. Otherwise we couldn't have for ex. transformers.

If we connect a coil to a voltage source, the voltage forces electrons in the conductor to move. The resistance isn't the only reason why the electrons do not get accelerated infinitely. If the current increases there's also the inductive emf which prevents infinite speeding. The equilibrium exists when the external voltage pushes electrons as strongly as the resistance and inductive emf together brake. 

The equilibrium can be an evolving state (note: I call changing current a state because it's determined) if the external voltage isn't constant, but changes. Actually every voltage changes at least when it's switched on, nothing has existed from minus eternity.

Differently changing voltages cause differently evolving equilibrium states which can be calculated by applying the induction law, Ohm's law and Kirchoff's laws.. That's solving a differential equation. Sinusoidal AC voltage causes sinusoidal current, as we surely know and its peak value is calculated by dividing the peak voltage with the total impedance.

Your case shortly: Inductive emf do not prevent current because the inductive emf exists only if current changes. The current will evolve in such way that inductive emf compensates the external voltage or actually compensates what's left,  when the resistive voltage drop is subtracted.