Jacob L. answered 02/03/20
Experienced tutor specializing in Biology.
To answer this question, you need to know a little about conductors. Assuming the wire IS a good conductor, it will have loosely bound electrons surrounding it.
Instead of thinking of a typical wire that you can hold in your hand, imagine a string of bonded silver and copper ions, over which electrons can flow. When a strong enough current (or difference in electric potentials) is applied, those negatively charged electrons will be able to freely flow to the more positive (or, less negative) charge.
You are correct in that there will be a sort of chemical change - the long term result of exposing a conductor to an electrochemical difference is called galvanic corrosion.
Just to note: this is not a very good question because it does not include the potential difference between the inside and outside of the cell (as this can vary greatly) or the metal(s) composing the wire. I think the instructor is wanting to make students realize that the electrochemical difference can be thought of as components of a galvanic cell.