Do electrons move in a conductor when it is connected to only one pole of a power supply? If I were to get a conductor e.g. a piece of copper wire or aluminium and connect it to one pole of a battery (let's take the positive pole for example), will electrons be removed from the conductor forming Cu or Al ions? Or does the flow only start when the circuit is completed?
I think as soon as a pole is connected, some physical change takes place. Let's say you connect both poles, there needs to be a potential difference, and I would think that difference would need to be "felt" by the other side for the electrons to flow. But if the second pole was only connected later, there needs to be a potential difference, so the metal would be charged (or I believe, ionised). Am I right in saying this?
Also, if electrons are flowing through a wire, can you say the wire is ionised, or am I getting this wrong?
 A: Let's start from the main question
Do electrons move when only one end/pole of the battery is connected ?

They do!  Let's say that you attach a wire to the positive terminal of the battery and this terminal is at "conventional" +5V. Imagine a lot of positively charged particles accumulated there, now electrons would move as near them as possible, creating the same +5V potential throughout the wire.
A very similar effect takes place in the charging of a capacitor by DC source, in that case too the circuit is never completed but we know that charges flow because that's how the capacitor charges.
I could only understand the other question as 
Does attaching conductors to battery or other sources of electrical energy ionize them?

It would be wrong to say that something like this happens, because when atoms get ionized they have quite a bit of freedom of movement for example $\text{Na}^+$ and $\text{Cl}^-$ in water are ionized and move freely similarly ions in hot plasma move about freely. While in conductors the concept of free electrons is accepted because electrons rather than completely leaving the atom, get into contact with several atoms and even though they leave a charged specie behind, that specie does not have freedom of movement and hence cannot be called ionized.
