"would it realistically make their suffering any less"
I think the best approach isn't to view Boycotts and fairtrade as a way of curtailing unethical industry, though hopefully that would indeed be the long term effect.
The reason for fairtrade is tat it creates an alternative market - or in other words an escape route.
Its our dollars that define the shape of the economy.
If we support fair trade industry, that will be where the entrepreneaurs will look for their opportunities and in turn, that will be the environment in which people in developing countries are employed.
We can create the alternative.
I am astounded that it hardly exists in the clothing industry.