Changing current limit on a cheap BLDC motor controller
There's a good chance - if you can find the current shunt and replace it with one of higher value. If the value is not known then you can measure it by passing a known current through the shunt (eg. 1A) and measuring the voltage drop across it. 

Current shunts are usually made from an alloy with low temperature coefficient. Do not be tempted to just use a length of copper wire, as to get sufficient resistance it will either be too thin (resulting in high operating temperature and increased resistance) or have higher inductance which might upset the current measuring circuit. 

Reducing the current limit (within reason) to protect a motor with lower current rating than the controller should have no serious side effects. If you go ridiculously low then FET switching currents may start to affect the measurement.