Does electricity flow in open circuits?
Keep in mind that the wire is a metal and thus already has a great deal of free electrons. The battery is not a source of electrons, it's a pump to move what is already there.

Still, you can view the system as a very small capacitor, with the wires being the plates. They would be relatively far apart and have very little surface area so the capacitance would be very very small. So, yes, I think there would be electron transfer, but it would be negligible and it would only last an instant.