It depends on inductivity:
I suspect the circuit would explode, with or without capacitor.
With just the battery - which also has zero inner resistance - the current would get infinite during the first 0 seconds. Except - while no energy is lost in heating wires - that would make the whole capacity of the battery.going into creating a magnetic field around the wire.
I'm not sure whether that would reduce the current in the wire, or not; Note this is unrelated to resistance.
If it does, the battery's energy goes into creating a magnetic field, during some time greater than zero.
And that's it!
We now have a completely normal superconducting electromagnet.
It will just store the energy of the battery forever (which is still part of the circuit),
In case the inductivity - causing the magnetic field to build up - does not reduce the current:
The infinite curent would create an infinite magnetic field, that creates infinite forces on the wire and resistor.
These have a mass greater than zero. So we have the - similar to the resistor - a perfect explosion.
Some people would call... wait, would have called it Apocalypse.
Regarding inserting the capacitor added after that:
In the first case, we will open the circuit - which makes our magnetic field break down, during finite time. This causes a voltage to be induced into the wire, with or without capacitor, but also make the wire move and bend a little, because of the changing magnetic field. There will be some more conversions between magnetic field and voltage/current, until all of the energy was spend on bending the wire.
In the second case, we already had an Apocalypse.
So: "It depends."