You aren't supposed to connect the terminals of a battery with a wire!
If you do, there will be a lot of current.
The wire will have some resistance so, yes, there will be a potential across it and so some current will flow in the resistor.
The way to analyze this would be to show the battery as a voltage source in series with an internal resistance. Add the shorting wire as a small resistance and the resistor in parallel with it. If you can estimate the internal resistance and the resistance of the wire, you can solve the circuit to find the current in the resistor.