Your original text admitted three interpretations, and I'm leaving the answers here:
1: What happens with a toy model when there's a circuit with an ideal battery and no resistance?
All the charge moves around the circuit at one moment in time (infinite current). The energy must leave the system as Electromagnetic radiation - accelerating charges radiate, and while that radiation would happen at any bends in the wire, it would probably happen most at the terminals where the charge goes from stopped to moving (and visa versa). The effect of energy leaving a system via EMR is often ignored in circuits, but basically, we've made a single signal broadcast antenna.
A battery represents two separate reservoirs of charge, so if charge moved between them on the terminal side, the battery would be a rock. Therefore, the work done by the current must happen between the terminals on the wire side. Don't worry too much about this scenario - there's no such thing as ideal batteries. Their internal resistance is orders of magnitude smaller than a circuit's resistance, and orders of magnitude larger than that of the wire.
2: What happens when I connect the terminals of a real battery with an ideal (superconducting?) wire?
Real batteries have internal resistance, so the battery will heat up and quickly either run out of charge or burn/explode.
3: What happens when I connect the terminals of an ideal battery with a real wire?
We specify battery voltage in circuits, so the current running through the wire will be high enough that when you multiply it by the resistance, you get back the battery's voltage. Also, the wire will heat up quickly and radiate light and heat until the ideal battery runs out of charge.
Some of the other answers included other ideas.
First, any circuit is a loop, so it will have an inductance. Inductance slows down the current in a circuit, but does not effect the circuit in steady state (or provide a real (pun intended) voltage drop). In the ideal battery/wire case, the inductance would cause the current to grow over time - that's nonsense because infinite current can't grow (you also need non-zero resistance to find the time constant - I don't divide by zero).
Second, we sometimes think of batteries as chemical capacitors. An ideal battery is not a capacitor. But if it were and there were an inductance in the circuit, the charge would move from one side to the other with an angular frequency of $(LC)^{-1/2}$. In response to the edit question, 'Will it discharge like a capacitor?', the time constant for an RC circuit is $RC$, so zero in this case. The battery won't send charges back the other direction in the circuit though because ideal batteries are not capacitors.
Incidentally, a capacitor also slows down the movement of charge, but it reverses the polarity, so the phase moves in the opposite direction. Also of note, whereas an inductor slows down changes in current most when they change most, a capacitor allows the freest flow of current when it is uncharged.
Lastly, it seems pretty clear that you're talking about a closed circuit, but if you weren't, well, nothing happens on open ideal circuits (unless they were recently closed, or will be closed soon).
Responding to other edits:
"If not, please tell me why the electrical circuit theory is meaningless without resistance."
I'm not sure what you're asking, but can we build circuits with just transistors, inductors, capacitors and diodes? I guess, but it'd be a lot more difficult to keep the magic smoke in. Circuits would also be a lot more difficult because we often model speakers, lights, motors and almost every useful thing in a circuit as a resistance. LC circuits (which have no resistors, but non-zero resistance) have a few important applications, but even so, we often put resistors in to dampen non-frequency signals or manage the voltage (with a voltage divider for example).
"If possible, can anyone give me [a fluid flow] analogy with a circuit with zero resistance, internal and external?"
I refer you to the Waterfall, though I had hoped for an aquatic image shaped more like Ascending and Descending. Water does not have an easy analogy for electromagnetic radiation because they are different phenomena. In another direction, flow of fluids is tremendously resistive, so perhaps the analogy you're looking for is that as fluids (and circuits) get colder, resistance goes down. The behaviors of both of these systems are subject to laws that are very foreign to our understanding as warm intuitioned creatures, and they won't help you in your circuits class.
It is not an issue of the field being conservative or not. Ultimately, Kirchhoff's laws are about the relationship between branch currents and node voltages in a network of lumped circuit elements. If you define three kinds of branch elements denoted by $R,C,L$ using the relationships $v=Ri$, $i=C\frac{dv}{dt}$, and $v=L\frac{di}{dt}$, respectively, then you may freely use Kirchhoff's current and voltage laws. These defining relationships between voltage and current are idealization and simplification not just for an inductor but also for a capacitor and resistor, as well. In the case of the inductor we ignore all fields outside the coil, and if we cannot because we have an inductive transformer then we include that part explicitly by defining a two-port with a pair of equations, such as $v_1=L_{11}\frac{di_1}{dt}+L_{12}\frac{di_2}{dt}$ and $v_2=L_{12}\frac{di_1}{dt}+L_{22}\frac{di_2}{dt}$, and a similar set of equations if you need more ports than two. If the capacitor is physically large then we may encounter problems with the current continuity law and will not be able to neglect the displacement current.
Note too that in no sense one could claim that the fields of a voltage or current generator are "conservative", not even for a battery: electrochemistry is not electrostatics. Somewhere, somehow you must impose a phenomenon that is outside of electricity or magnetism. Instead we postulate that certain node pairs have a predefined voltage history, and a given branch has a predefined current history independently of the rest of the circuit and thus represent a voltage or a current source, resp. In other words sources are time dependent boundary conditions. This way as you go around in a loop you must always get 0 voltage, no conservative field is needed. At the next level of abstraction you only need that in an arbitrary loop at any instant every connecting wire the current must be the same. And assuming linear superposition you can derive that the sum of branch currents at any node must be zero. So then the only questions is whether a loop is physically small enough so that the current uniformity holds. Once you have picked the defining lumped element equations between $v$ and $i$ you may say that KVL and KIL have more to do with network topology than actual physics.
Best Answer
No, for an ideal inductor, the inductor emf $\mathscr{E}_L$ is, at all times, equal in magnitude and opposite in sign to the voltage $v_L$ across the inductor.
$$v_L = L \frac{di_L}{dt} = -\mathscr{E}_L$$
But I am curious about the line of reasoning that led you to believe the inductor emf behaves as you describe. Would you edit your question to include it? It might be valuable to others.
Also, I've answered, in more detail, a few related questions here. I'll look them up and post links later.