A train transformer may, or may not, not have enough ampacity or voltage to light up the cutting wire. But that depends on the total resistance of the wire that is being used.
Watts = amps x volts. If the transformer has an output voltage of say...12 volts, its output capacity is 5 amperes then the maximum output is 60 watts. That would be enough to light up a very short and very small diameter wire.
An ordinary automotive battery charger is likely to have a lot more output capacity than the train transformer.