Will electricity flow in a perfectly conductive medium?
Yep, basically you're thinking about this wrong.

Ohm's law basically says: "for a resistor in isolation, you can relate Voltage, Current and Resistance." in other words if you know any two of those quantities you can determine the third one.

There is nothing more to it.  In this case, you know the ideal resistance = 0 and you have some amount of Current = I.  In the case of an ideal conductor you have Zero voltage drop across it, this comes from:

\$ V = I * R \$ 

\$V = I * 0\$

\$ V= 0 \$ 

What is telling is your statement "... that since resistance is required for a potential difference to build up ... "

That is the core of your misunderstanding and the core of where people go wrong.

A resistor in isolation is pretty useless, it isn't even a circuit. So a resistor cannot just decide to produce a voltage to if it is flowing a certain amount of current. So there is no voltage in the resistor to "build up" that voltage is imposed by the other other components in the circuit only.

An ideal Voltage Source will provide a fixed voltage and will flow as much current as possible to maintain that voltage.

An ideal current source will flow a fixed current and will provide as much Voltage as possible to ensure that current flows.

Your statement implies that the resistor generates the voltage.  In reality if you drive a resistor with a current source, the current source itself will generate the voltage necessary to maintain the current and since it is a resistor, you can't have a certain amount of current without also providing the voltage.

Of course I'm talking to ideal components here, but this is still useful.

So the answer is, in a superconductor you will get zero voltage drop along the length of the conductor.