Consider what would happen if it didn't. The pressure on the material in the hole would increase; but that is true for ANY hole, so it would be true for the entire bulk of the material. This would only happen if the material was confined and could not expand itself. So of course, the hole will expand precisely in accordance with the equations describing the expansion of the bulk material.
But there is no material IN the hole. Therefore the area of the hole will not expand, only the material surrounding it.
In fact the material surrounding the hole will expand at a faster rate that the material (none) in the hole. My money is that the hole will be squeezed by the material surrounding it and shrink.
Expansion joints on railway lines close up when the line heats up (but they are not an integral part of the material. On the other hand a hole in a piece of rubber expands as the rubber is expanded, but that is an external force stretching the rubber.
What was I thinking? Of course the hole expands - basic metalurgy. How else would steel tyres be expaned to fit on wagon wheels, metal rivets shrunk to make water-tight seals between plates? Focussed on the wrong thing and then overthought it.
During a thermal expansion or contraction, any hole in solid behaves as if it were full of the same material. Therefore the diameter of your hole will increase according to the expansion coefficient of the copper.