I presume everyone (like me) is waiting for you to reason first before they answer outright.
in reactions with electron transfer, look at the table of standard reduction potentials first to see what would have any chance of happening. Then reason if it could in your given situation.
Show us what you THINK will happen in Mg|CuSO4|Cu
I really don't understand what will happen if I use Mg and Cu as electrodes with NaCl as electrolyte@.@. I don't need to concern about electrode potential because it is out of syllabus... I don't think Sodium ion will reduce to become Na(s), but I just can't think of anything else which could reduce. However, the fact is that NaCl can be used as electrolyte in this chemical cells, so I think there must be something to accept the electrons from the external wire. I really can't figure out what it is and what would happen if Magnesium Sulphate is used in Mg/Cu cell.
For your question (Mg/Cu in copper(II) sulphate electrolyte), I am certain that copper(II) ion from the solution will reduce to Copper at cathode while Mg electrode gives up Mg ion to the solution. However, I don't really know what would happen if I use Magnesium Sulphate instead. I think there should be some reaction because it fits the basic criteria of a chemical cell --> different metals, electrolyte. I am thinking about that as Mg electrode release electrons to form Mg ion, then the Mg ion will flow to cathode to accept the electron to become Mg again, forming on another electrode. This is my thought, however, I don't feel comfortable about this. I think there must be something wrong.
Thanks